Secretary of State George P. Shultz is scheduled to go to Vienna May 15 for the 30th anniversary of the signing of the Austrian State Treaty, which restored the sovereignty of Austria after World War II. The trip will provide an occasion for a meeting with Soviet Foreign Minister Andrei Gromyko, according to the State Department.

State Department spokesman Bernard Kalb, referring to the Shultz trip, said yesterday that "you would not rule" out a meeting with Gromyko. He noted that at the 25th anniversary celebration in 1980, then-Secretary of State Edmund S. Muskie held a lengthy meeting with the Soviet foreign minister.

Austrian Embassy sources said indications are that Gromyko will be in Vienna for the May 15 observance. The British and French foreign ministers, whose countries also signed the treaty, are expected to attend along with foreign ministers of countries adjoining Austria.

Shultz had been urged to attend the observance by Western European foreign ministers, who said a meeting with Gromyko in mid-May might spur nuclear- and space-arms negotiations in Geneva. Shultz also would be likely to discuss with Gromyko a possible summit meeting of President Reagan and the new Soviet leader, Mikhail Gorbachev, State Department officials said.