A 64-year-old Michigan clergy-woman yesterday was elected a bishop of the United Methodist Church, the first woman to hold such a post in a major religious denomination in nearly 2,000 years of Christianity.

The Rev. Marjorie Matthews, who has been district superintendent for the church in Traverse City, Mich., for the past five years was chosen in a dramatic election in Dayton, Ohio, that went to 29 ballots.

In a press conference immediately afterward Matthews called her victory, "a gigantic step for woman-kind . . . a leap in the church's understanding of theology."

In the United Methodist Church, the second largest Protestant body in this country, bishops are elected by lay and clergy delegates to regional assemblies called Jurisdictional Conferences. Bishops are elected for life, but they serve for four-year terms in various parts of the country. Because of church retirement rules, Matthews will serve for only one term.

Matthews entered the ministry only 15 years ago from a job as an assistant to the president of an automotive parts manufacturing firm. After serving half a dozen churches, most of them in her native Michigan, she was named to the supervisory post of district superintendent, with responsibility for a county or more.

Matthews, who holds three graduate degrees, is divorced and has one son and four grandchildren.

The move to open up decision-making roles in the United Methodist Church to women has paralleled the women's movement in general over the last 12 years. Although a woman -- theologian Georgia Harkness -- won votes in a bishops' election as far back as 1948, a well-directed effort to get a woman elected four years ago failed.

In the wake of that defeat, organized feminist forces in the 9.7-million-member church decided to retrench and groom candidates for the 1984 election, instead of risking another defeat this year, according to one source. Elections are held every four years to fill vacancies caused by deaths or retirements.

But as this year's election drew near, liberals in the churches in the Methodists' North Central Jurisdiction organized behind Matthews.

In one of the hardest fought bishops elections in the church's history, officials decided to suspend the rules after 29 ballots yesterday to break the deadlock that had developed between Matthews and the Rev. Emerson Colaw, 58, of Cincinnati.The two were named by acclamation to the two posts that remained to be filled.

It remains to be determined where the new bishops will be assigned, but according to church rules, their first assignment cannot be in their home area. a

The North Central Jurisdiction includes Michigan, the Dakotas, Minnesota, Iowa, Wisconsin, Illinois, Indiana and Ohio.

In the United Methodist Church, virtually all ecclesiastical authority is vested in the 45 active bishops, who preside over jurisdictions that can range from several states to a metropolitan area, depending on the density or church membership. They are responsible for both the administration and spiritual life of the church in their area, with the authority to assign clergy as they see fit.

In recent years, the church has responded to demands for a larger role for women -- deciding in its national General Conference eight years ago that at least 40 percent of the leaders of its national boards and agencies must be women.