The United Auto Workers union, one of North America's premier labor organizations, is breaking up because of what its leaders say are irreconcilable differences between its U.S. and Canadian branches.

The split was announced in Dearborn, Mich., late Monday night after the union's international executive board rejected a Canadian demand for more freedom in the nearly 50-year-old relationship.

U.S. and Canadian UAW leaders speculated yesterday that the institutional divorce will become final by May 1986, when the UAW holds its next constitutional convention.

Costs, property rights and other matters have to be worked out, the UAW officials said. Afterwards, the Canadians will be free to pursue their own course with the U.S. auto makers who dominate the North American car industry. The UAW, which has lost 170,000 members in the United States since 1979, will be reduced to 900,000 in North America with the departure of the Canadian branch.

Auto industry analysts and officials said yesterday that the split was long in coming. They said that the breakup is attributable as much to changes in the international auto industry as it is to growing nationalism in Canada.

"This is all a part of a long-term process that began in the 1970s," said Martin Anderson, co-author of a recently released book on the future of the automobile industry and an analyst with Sector Research in Boston.

Because of differences in foreign exchange rates, government laws regulating the workplace, manufacturing processes and other factors affecting the business of the international auto industry, "there is a tremendous international pressure on unions to decentralize," Anderson said.

Leaders of the Canadian UAW, who represent 120,000 members, said they were reacting to that pressure last October when they staged a 10-day strike that shut down General Motors Corp. plants in Canada and, as a result, in the United States as well.

The strike was called after UAW-Canada Director Robert White rejected a new labor agreement -- one emphasizing job security over wage increases -- that was ratified by the UAW in the United States.

White said that the U.S. agreement "was not realistic for Canada." U.S. auto makers enjoy a $7 hourly labor-cost advantage in Canada largely because of differences in U.S.-Canadian exchange rates, White said. The Canadians held out for more and got $1.14 an hour more than their U.S. peers in a new three-year contract with GM.

White charged that attempts by the UAW's U.S.-based international leadership to persuade the Canadians to accept U.S.-style settlements amounted to interference in Canadian bargaining.

White made four specific demands, all of which were rejected by the board:

* The right of the Canadian UAW director to have direct access to and control over UAW strike-fund allocations for Canada.

* The right to pursue mergers with unions in Canada, including Canadian branches of other U.S.-based unions, whether or not such mergers would be deemed feasible in the United States.

* An end to "interference" by the international union in collective bargaining in Canada.

* Elimination of the requirement that Canadian-UAW staffers report to U.S.-based divisional heads.

"We deeply regret that the Canadian leadership has presented this board with a set of demands which conflict with the letter and spirit of the UAW constitution and which, if granted, would cause the UAW to cease to exist as an international union in any meaningful sense," the majority of the union's board members said after rejecting White's demands.

U.S. auto makers, who operate some 30 assembly and parts plants in Canada, generally were reticent about the breakup of the UAW. But John F. Smith Jr., General Motors of Canada's president and general manager, hinted strongly that GM might choose to scale back its investments in that country if White's group becomes more militant.