Dr. Sidney Harman, an innovative businessman who believes in letting workers share power with management in industrial plants, was named under secretary of commerce yesterday by Jimmy Carter.

Harman made his fortune in the high-fidelity business, with the firm Harman-Kardon, Inc. He is chairman of Harman International Industries, Inc., a conglomerate.

One of its subsidiaries is a firm that makes auto mirrors in Bolivar, Tenn. That plant is run by a management committee composed largely of shopfloor workers, and Harman has said it is a highly profitable endeavor.

If confirmed by the Senate, Harman will serve under Juanita Kreps, the Duke University professor whom Carter has designated Secretary of Commerce.

In another development, wellplaced sources said Columbia University law professor Richard Gardner has been selected as ambassador to Italy. He would replace John A. Volpe, who resigned yesterday.

Gardner was an early Carter backer who reportedly had hoped for a higher post in the administration. He has taken part in numerous international conferences and negotiations, and lectures widely on the world's new generation of problems - food, environment, energy and interdependence, among others.

Sources said former Rep. Patsy Mink (D-Hawaii) would be assistant secretary of state for oceans and international environmental and scientific affairs.

Mink would be the second woman chosen for a high State Department post under Secretary-designate Cyrus R. Vance. Vance previously has picked Lucy Wilson Benson to be under secretary for security assistance.

Mink, 49, represented Hawaii in the House from 1964 through last year. She was defeated in the Democratic primary for the Senate and has been pushed by various women's groups for a high post in the Carter administration.

Another former member of Congress, Sen. Gale W. McGee (D-Wyo.), will be named American ambassador to the Organization of American States, sources said. McGee was defeated for re-election last November.

McGee was chairman of the Senate Foreign Relations Committee's Subcommittee on Western Hemisphere Affairs and so has a background in Latin American matters. The OAS ambassador is based in Washington.

The Los Angeles Times reported these additional likely appointments in the State Department: Sol Linowitz, a former ambassador to the OAS, to be Panama Canal negotiator in place of Ambassador Ellsworth Bunkers; Carol Laise, Bunker's wife to retain her post as director general of the Foreign Service; and Barbara M. Watson, to return to head security and consular affairs.

Watson from 1969 to 1974 was the highest ranking black official in the State Department. Appointed by President Johnson to the security-consular bureau, her removal from that post during the Ford administration brought angry protests from the NAACP and the Congressional Black Caucus.

The Times also said Dr. Peter Bourne, a Washingto psychiatrist who served in Carter's presidential campaign and in his Georgia administration, will oversee narcotics problems.

Washingtonian Clifford Alexander. an unsuccessful candidate for mayor in 1974, is a leading candidate for an important Pentagon jobM perhaps Secretary of the Army, well-placed sources said yesterday.

Alexander, an attorney in private practice here, could not be reached for comment. Friends said he had not yet been offered a job, but had been approached by the new administration.

If named to the Army post, Alexander would be the first black to head one of the three services. A 43-year-old graduate of the Yale Law School, Alexander worked in the White House under Lyndon B. Johnson.

Carter's press secretary, Jody Powell, announced yesterday that Jack H. Watson Jr. will represent Carter before various groups around the country.

Watson, who is also expected to be a sort of Cabinet secretary in the White House, has headed the Carter transition team here.