The Social Democractic Party of West German Chancellor Helmut Schmidt suffered a major loss today in a West Berlin municipal election that could strain seriously his federal coalition government.

Partial returns indicated that the balloting in the metropolis would end in a stalemate among four parties, with none winning an absolute majority. The opposition Christian Democrats won a pluarlity, but the future leadership of the city was in doubt.

Acting Mayor Hans-Jochen Vogel, the Social Democratic candidate for reelection, acknowledged the defeat and said he would not contest when the new legislature meets to elect a mayor.

The result represented a blow to Schmidt, whos party had controlled Berlin almost without interruption since World War II. It comes at a time of multiple troubles for the West German leader.

Preliminary official results gave the Social Democrats 38.4 percent of the vote, down from 42.7 percent in the last election two years ago; their partner Free Democrats 5.6 percent, compared with 8.1 percent last time; the Christian Democrats 47.9 percent, up from 44.4 percent last time; and the Alternative List coalition 7.2 percent compared to 3.7 in 1979.

This would give the Christian Democrats 65 seats in the 133-member legislature, the Social Democrats 52, the Alternative List 9 and the Free Democrats 7.

Party Chairman Willy Brandt, a former Berlin mayor, called the loss "bitter," but refused to take it as a comment on Bonn government policy.

The Christian Democrats heralded the vote as a political watershed. The party chairman, Helmut Kohl, said it was a defeat for Schmidt as well as for the acting mayor, Vogel.

Richard von Weizsaecker, head of the city's Christian Democratic Union, said he expected to become mayor. He told an interviewer his party would hold talks shortly with both the Social Democrats and Free Democrats -- who had ruled as a coalition until now -- about forming a new coalition.

But Vogel ruled out participation in any coalition arrangement.The Free Democrats appeared divided on whether to swing into a new government with the Christian Democrats in view of the impact this might have on the future of their coalition with the Social Democrats in Bonn. This raised the possibility of another election in the autumn.

The Berlin impasse, which had been forcast by preelection surveys, is due largely to the success of the so-called Alternative List -- a collection of many autonomous environmental and mostly left-wing activist groups that for the first time gained the minimum 5 percent of the vote needed for representation.

The group has ruled out a coalition with any other party, and the other parties have said they would not consider alliances with it.

The steep drop in votes for the Social Democrats reflected at the least a widespread disaffection with the party's programs and character in Berlin. The election had been moved forward two years following the collapse in January of the government of mayor Dietrich Stobbe in connection with a major financial scandal.

Vogel, who had been rumored as Schmidt's likely successor, left his post as justice minister in Bonn to be interim mayor in Berlin. According to opinion polls, the 55-year-old Vogel was more popular than the professorial Von Weizsaecker, 61.

The campaign focused on such local problems as the occupation of vacant houses by squatters. The housing protest, meant to dramatize a severe shortage of apartments, was accompanied by often violent demonstrations.

With the shadow of scandal, the party's policies looked discredited to many voters. Party leaders engaged in considerable self-criticism during the campaign, pressing the theme of party renewal.

The strong showing of the Alternative List was seen as a product of voter dissatisfaction with the three parties that had made up the Berlin legislature. The grouping draws mostly young members from educational, cultural and protest circles. Its symbol is a green hedgehog that, probably not by accident, faces left on posters that describe the bloc's chief purpose as "fundamental opposition."

In the campaign, which was generally free of animosity, Vogel, attempting to disengage from Social Democratic policies of the past, preached credibility and courage for new ideas. He stressed his past experience as a government manager -- he was mayor of Munich for 12 years.

Von Weizsaecker argued the need for change. His urbane manner fit with the image projected by the Berlin Christian Democrats of a still conservative but modern, big-city party.