Georgi A. Arbatov, the Soviet Union's leading expert on U.S. affairs, is speaking to the American public in a series of lectures and luncheons in Iowa this week but, under a State Department order, he is forbidden to speak to the news media.

The object of the unusual restriction is chief of Moscow's Institute of U.S. and Canadian Studies and a senior Kremlin adviser, who is in this country at the invitation of Grinnell College in Iowa and the Dartmouth Conference, a private forum on U.S.-Soviet relations.

Associate Professor Robert Grey, Arbatov's host at Grinnell, said the restriction became known when Arbatov declined to be interviewed by a waiting United Press International reporter on arrival Sunday at Des Moines airport.

A scheduled news conference with Arbatov at the college Monday was canceled because of the restriction. However, Arbatov agreed to be interviewed by The Des Moines Register and Iowa public television on grounds that the restriction does not apply to "local media."

State Department press officer Anita Stockman said Arbatov had been informed that "any contact with the media would be contrary to the purposes for which his visa had been issued." The approved purposes were lectures and research.

Stockman said the action was based on reciprocity, because "no American spokesman for U.S. positions has received similar access to the Soviet media for some time."

Reagan administration officials have been irked at news appearances and interviews by Arbatov, a major Kremlin spokesman on U.S. affairs and a policy adviser considered close to Soviet leader Yuri V. Andropov.

In April, 1981, the State Department refused to extend Arbatov's U.S. visa to permit him to appear on a U.S.-Soviet debate on public television. Nonetheless, he has given many press interviews in Moscow, and has appeared often on U.S. television via satellite, most recently April 3 on ABC-TV's "This Week with David Brinkley."

According to Grey, Arbatov spoke to 1,100 people in a public lecture at Grinnell Monday night and was giving another major lecture there last night. Additional public appearances, including breakfasts, luncheons and lectures, are scheduled in Des Moines and Iowa City. Nearly all of the events are open to the press, and reporters in most cases are free to question Arbatov during question-and-answer periods.

Grey said he found the restrictions "ironic and regrettable" in view of U.S. traditions of freedom of speech and the press. "It's also rather stupid when there are a whole series of public lectures," he said.

Arbatov was unavailable for comment but, according to Grey, said in a question-and-answer session at Grinnell, "Your State Department would rather I not talk very much to the media."