South African police today arrested Allan Boesak, one of this country's most prominent nonwhite political leaders, on the eve of a mass march he planned to lead on the prison holding Nelson Mandela, the black underground leader.

The arrest came as the economic repercussions of South Africa's deepening political crisis caused the country's already plummeting rand to fall about 10 percent today to a record low of 36.65 U.S. cents. Finance Minister Barend du Plessis closed the foreign exchange market and the Johannesburg Stock Exchange until Sept. 2 because of a run of foreign-bank demands for debt repayments.

As Boesak's arrest brought angry protests from church leaders around the world and increased racial tensions in Cape Town, other organizers of the expected 20,000-strong march, which the government has vowed to stop with force if necessary, said it would go on as planned.

Some expressed fears that without Boesak to control the crowd, the danger of a violent confrontation would be greater.

Boesak, who is president of the World Alliance of Reformed Churches and whose standing in the nonwhite community approximates that of the Nobel Peace laureate Desmond Tutu, was arrested under the most stringent of South Africa's security laws. It provides for indefinite imprisonment in solitary confinement without charges and without access to family or lawyers.

[In Washington, State Department spokesman Charles Redman said the United States had formally protested Boesak's detention to the South African government. Redman said such actions "can only exacerbate the current cycle of polarization and tension"]

As news of the arrest spread through Cape Town's black and mixed-race townships, groups of youths began rioting and stoning cars; the police closed roads leading into some of the townships.

Warning that the Christian community worldwide would react with "deep emotion and anger" to Boesak's arrest, the secretary general of the church alliance, Edmond Perret, said in Geneva tonight that he will fly to South Africa Wednesday to try to see Boesak.

Boesak, a member of the mixed-race, or Colored, community, founded the United Democratic Front, an alliance of more than 700 black community organizations that the government claims is behind the unrest that has resulted in more than 625 deaths in the past year.

Police have arrested 32 leaders of the front since Friday, and 38 others have been charged with treason, which is a capital offense in South Africa.

It was widely believed that Boesak, who holds the title of patron of the front, enjoyed a measure of immunity from arrest because of his international status.

His arrest reflects official concern about the challenge to its authority that the Wednesday march would present. Law and Order Minister Louis le Grange has issued repeated warnings in the past three days of his determination to stop the march, telling "innocent people" to keep clear of the route so they do not get hurt.

White leaders of Boesak's Dutch Reformed Church sent him telegrams today urging him to call off the march. But the theologian, who has been trying to develop a strategy of civil disobedience in Cape Town, remained determined to go ahead with it.

He was arrested soon after addressing a packed meeting of students at Cape Town University, many of whom pledged to join the march. He was stopped at a roadblock on his way to the Colored University of the Western Cape, where 17 student leaders involved in organizing the march had just been arrested.

Boesak's wife, Dorothy, said tonight the police had told her about the arrest but refused to say where her husband was.

The general secretary of the South African Council of Churches, C. F. Beyers Naude, said tonight he doubted whether the government realized the degree of anger Boesak's arrest would arouse in Christians worldwide.

James Andrews, the stated clerk of the Presbyterian Church and a colleague of Boesak in the World Alliance of Reformed Churches, said the denomination had sent messages to both President Reagan and South African President Pieter W. Botha urging the theologian's release, according to United Press International in Washington.

Separate but similar messages were sent by the American Lutheran Church, the Lutheran Church in America and the Association of Evangelical Lutheran Churches.

[In Geneva, the executive committee of the Lutheran World Federation interrupted a meeting to issue a statement demanding Boesak's immediate release.]

As tension rose in Cape Town and unrest continued in other parts of the country, Botha made a surprise tour of black townships in the eastern Cape Province, the scene of the worst race rioting of the past eight months.

He met some of the black counselors who have been targets of attack by activists who regard them as collaborators because they hold office under the system of administration established by the white-minority government.

Botha said after his tour that he had been impressed by his friendly reception and "the strong spirit of cooperation" he had sensed in the townships.

He said the blacks he had met welcomed the state of emergency his government declared five weeks ago and urged him not to lift it until the unrest ended.

Announcing the closure of the foreign exchange market and the stock exchange tonight, du Plessis said there had been "abnormal pressure" on the capital account of the country's balance of payments recently for "reasons unrelated to the healthy underlying economic conditions."

He said steps would be taken between now and Sept. 2 to enable South Africa "to meet all its international obligations." Economists said this meant South Africa needed to negotiate a rescheduling of foreign loans because of the sharp drop in the rand's value.

In 1980 the rand was worth $1.34, by early 1984 it was down to $0.80, and today it was quoted at $0.36.

In an unrelated development, the government announced a reprieve for two black communities threatened with forced removal under a policy of consolidating tribal "homelands." The adjoining communities of Driefontein and KwaNkema in eastern Transvaal Province are classified as "black spots" in the 87 percent of South African territory reserved for white ownership. They were ordered to move 80 miles from the farmland they have occupied for more than a century.

Community leaders resisted the removal orders for three years, losing court battles because of the government's wide powers under the apartheid laws.

Today's unexpected announcement came after Ben Wilkens, a deputy minister at the black affairs ministry, talked with leaders of the two communities yesterday. Wilkens gave no reasons for the government's change of mind.

Ending forced removals has been a major theme of the Reagan administration's policy of quiet diplomacy with Pretoria. The South African government has relocated more than 2.5 million blacks in the past 20 years.

Meanwhile, police headquarters announced tonight in Pretoria a reduction in unrest reports from Wednesday on. A statement said this was because the number of incidents had declined, an observation that did not seem borne out by reports from around the country. These told of unrest in at least six centers, with the stoning of vehicles, the fire-bombing of a home and the burning of two schools.

At Bethal, in eastern Transvaal Province, police clashed early today with a crowd gathered for the funeral of an unrest victim. Witnesses said the police fired tear-gas cannisters into a tent where mourners were congregated.

Meanwhile, Foreign Minister Roelof (Pik) Botha warned that a visit to South Africa this weekend by ministers from Italy, the Netherlands and Luxembourg might be blocked. The three ministers had hoped to visit Mandela, but that visit has been ruled out. Speaking in Johannesburg, Botha seemed to be reacting to statements from European Community foreign ministers condemning apartheid.