Douglas A. Fraser, 60-year-old vice president of the United Auto Workers, has been selected by his fellow officers to succeed Leonard Woodcock as president of the UAW, one of the nation's largest and probably its most influential union.

Woodcock, who is retiring, announced yesterday that he had met with the top UAW officers during the holidays and that all of them had decided to support Fraser. Three other vice presidents had been considered candidates for the job, but Woodcock said they "are not pressing their candidacies.

Woodcock did not formally endorse Fraser, but union sources said he only held back because he did not want to appear to be forcing the UAW to select Fraser. The union convention in May will formally select the new president.

Fraser, who is in charge of the UAW's Chrysler division, almost became president of the union in 1970, when a successor who chosen for Walter Reuther, longtime union president who was killed in a plane crash. But the executive board favored Woodcock over Fraser by a 13-to-12 vote.

Like Woodcock, Fraser was a protege of Reuther. In the past he has called himself an "ultraliberal" and he makes no bones about his progressive politics.

Fraser came to the United States from Scotland when he was 6. He went to work in a Chrysler plant at the depths of the Depression, right out of high school. He has become one of the country's most articulate and highly regarded labor leaders.

Fraser believes that the needs of workers cannot be met solely at the collective bargaining table. Comprehensive national health care, for example, cannot be provided simply by employers, Fraser said in an interview last fall, "so increasingly we'll be turning to political action."

Fraser also believes that the work week will have to be shortened. "I think it's absolutely inevitable in our country that there has to be a reduction in work time generally," he said in the interview.

Fraser has been active in the UAW's political activities in Michigan and is expected to speak out often and forcefully on national issues as president of the union. Woodcock has brought a professorial demeanor to the job, but Fraser is known as live-lier and more outspoken.

Woodcock was a leading contender for a Cabinet post in the Carter administration, perhaps as Secretary of Health, Education and Welfare, but he asked that his name be withdrawn from consideration. Under the union's rules, Woodcock - who is 65 - could not be re-elected president this year.

Fraser has been the front-runner to succeed Woodcock since the latter became UAW president. The other man most often mentioned as a possible president is Irving Bluestone, vice president of the UAW's General Motors division and a respected intellectual within the union.

But Bluestone was one of those who decided to back Fraser, according to Woodcock's announcement yesterday. Bluestone will run for re-election at the May convention, Woodcock said.

So will Ken Bannon, Vice president of the Ford division, and Pat Great-house, vice president of the American Motors division, Woodcock said.

Woodcock made his announcement yesterday in his capocity as chairman of the "administration caucus," the most powerful of the UAW's internal political factions. Other factions are expected to run candidates against Fraser at the May convention, but union forces said it was virtually impossible for Fraser to be defeated.

The same sources said Fraser had emerged as the clear favorite for the presidency in a series of meetings Woodcock has been holding with top union officers over the past four weeks.