The Reagan administration yesterday imposed new restrictions on currency transactions that will sharply limit U.S. tourist and business travel to Cuba. It said Cuba cannot be permitted to earn U.S. currency while it is "actively sponsoring armed violence against our friends and allies."

The State Department described the rules as being intended to tighten the economic embargo against President Fidel Castro's government. They were announced with a flourish of tough rhetoric reminiscent of the threat by Secretary of State Alexander M. Haig Jr. to "go to the source" in combating alleged communist aid to leftist guerrillas in El Salvador and elsewhere in Central America.

Specifically, the restrictions will bar most Americans from using U.S. currency or credit cards to pay expenses related to travel to or from Cuba. The Treasury Department, which promulgated the rules under the authority of the Trading with the Enemy Act, said penalties for violations could involve as much as 10 years in prison and a $10,000 fine.

Exempted from the restrictions are Cuban Americans with relatives living on the island. Such persons now comprise about half of those traveling to Cuba. Also exempted will be journalists and "bona fide researchers."

Haig and other senior administration officials have spoken occasionally about possible new action to increase the effects of the U.S. embargo that has been applied against Cuba since the early 1960s. However, the timing of the U.S. move came as something of a surprise.

Last month, Haig authorized Mexican Foreign Minister Jorge Castaneda to sound out Cuba and Nicaragua on negotiations to end support that the United States charges they are providing to the Salvadoran rebels. Both governments have publicly expressed willingness to begin talks, and the United States two weeks ago even made an eight-point proposal for discussion with Nicaragua.

However, administration sources said last week that Nicaragua, which the United States contends is under Cuban influence, does not seem sincere about negotiating an end to the alleged arms flow. The sources added that the administration plans to try putting more pressure on Nicaragua before it agrees to begin talks.

It was not immediately clear whether the action against Cuba is part of this campaign to force Nicaragua and, indirectly, those countries supporting it, to be more receptive to U.S. demands. But a statement accompanying announcement of the currency rules revived Haig's charges that the conflict in Central America is part of a global, East-West confrontation.

It said, "Cuba, with Soviet political, economic and military support, is increasing its support for armed violence in this hemisphere.

"In the face of Cuba's increasing attacks on freedom, self-determination and democracy, our economic embargo is being tightened. Numerous measures are under consideration designed to make Cuba more fully bear the costs of its adventurism."

It added, "Cuba will not be allowed to earn hard currency from American tourists at a time when Cuba is actively sponsoring armed violence against our friends and allies."

Restrictions on travel to Cuba were eased substantially by the Carter administration in 1977. Assistant Treasury Secretary John Walker said yesterday that about 40,000 people visited Cuba from the United States last year and that approximately 17,000 to 18,000 of that number would have been barred under the toughened currency rules.

Walker said he could not estimate how much the new regulations might cost Cuba in U.S. dollar earnings.