President Carter has approved a meeting in Vienna May 16 between incoming secretary of state Edmund S. Muskie and Soviet Foreign Minister Andrei A. Gromyko, administration sources said yesterday.

Muskie, who is expected to be confirmed by the Senate and sworn into office by then, also is to meet with foreign ministers of America's 14 partners in the North Atlantic Treaty Organization in Brussels earlier the same week, the sources said.

White House approval of the Muskie-Gromyko meeting ends a period of uncertainty about the U.S. attitude toward such a Soviet-American session, which would be the first at the top level since the Russian invasion of Afghanistan Dec. 27.

The question of a high-level meeting was reported to be unresolved at the time Carter accepted the resignation of Cyrus R. Vance as secretary of state.

Vance had favored meeting with Gromyko earlier this year, when it was believed that Yugoslavian President Tito was about to die and both U.S. and Soviet foreign ministers were expected in Belgrade for the funeral.

At that time, according to a White House official, there was disagreement about the matter in high policy councils, with Carter's national security affairs adviser, Zbigniew Brzezinski, opposed.

Last weekend Brzezinski told a BBC interviewer, "We'd be glad to talk to the Soviets but [it] has to be focused on a relationship based on mutual restraint and reciprocity."

U.S. officials pointed out that the Soviets must also approve a Muskie-Gromyko meeting for it to occur. The Russians have inquired about a meeting with the United States May 16, when Gromyko will be in Vienna to commemorate the 25th anniversary of the Austrian Peace Treaty, but have not made an explicit request.

Meanwhile, reliable sources said State Department spokesman Hodding Carter, who has become a celebrity through his televised daily briefings on the Iran crisis, plans to quit his post on July 1.

Carter, who holds the dual positions of spokesman and assistant secretary for public affairs, apparently will be the first of Vance's loyalists to leave the department in the wake of Vance's resignation.

When Vance's resignation was announced formally Monday, Carter, in response to Vance's plea that key department officials remain at their posts, said he would stay on for the time being. Earlier, there has been rumors that he would resign in sympathy with Vance's protest over the ill-fated attempt to rescue the American hostages in Iran.

However, the sources said, Carter has made clear that he will stay only until Muskie completes his transition into the secretary's job. Carter has indicated that he would like Muskie to have a replacement on hand so that he can leave by July 1, the sources added.

Acting Secretary of State Warren M. Christopher indicated Wednesday that he would like to leave after the transition, and said he believes Muskie should be free to choose his own principal deputy. However, the sources said, President Carter and Muskie plan to confer with Christopher and explore the possibility of his changing his mind.

Also expected to leave the State Department in the near future is Hodding Carter's wife, Patt Derian, who has served throughout the Carter administration as the controversial and outspoken assistant secretary for human rights and humanitarian affairs.

However, the sources said, Derian still is undecided about whether to leave at the same time as her husband or stay on for a longer period in an effort to influence the future course of the human rights policies under her direction.

Hodding Carter, who came into the administration from a background as a small-town Mississippi newspaper editor and civil rights activist, quickly established himself as one of Vance's most trusted lieutenants.

His access to Vance, coupled with an affable, easygoing manner, made him very popular among reporters covering the foreign policy area, and he gained a reputation as one of the most able and influential spokesmen in the history of the State Department.

However, he always was known as an individual whose first loyalty was to Vance, and he had made clear that he would leave the department when Vance did -- originally expected to be at the end of this year, when President Carter's term of office is over.

The sources said Muskie plans to bring to the State Department two of his key Senate staffers: Leon G. Billings, his administrative assistant, and Robert R. Rose, his press secretary.

According to the sources, Billings will act as Muskie's executive assistant in the secretary's office, and Rose will be assigned duties as a speechwriter on Muskie's personal staff.

The souries added that Muskie tentatively plans to leave the rest of his Senate staff, except for his two personal secretaries, in place on Capitol Hill so they can provide a support nucleus for whomever is appointed to fill out his term (which expires in 1983) as senator from Maine.