Bowing to growing public concern and political uncertainty about nuclear energy, a state government in West Germany today indefinitely postponed plans to license construction of the country's first nuclear reprocessing plant.

The decision by the State of Lower Saxony dealt a potentially crucial setback to the federal government's plans to move cautiously ahead with an already sizable nuclear power program. It also in effect shelved the major part of what would have been the world's largest commercial nuclear complex - a huge $6 billion combined reprocessing plant and nuclear waste disposal center.

The center would have been near the small town of Gorleben in northern Germany near the East German border. The town's name in the past year or so, and especially since the nuclear accident at Three Mile Island, has become synonymous with the anti-nuclear power movement in West Germany.

In announcing the decision on the reprocessing plant, state governor Ernst Albrecht, a Christian Democrat, made clear, however, that work will continue on a drilling project to see if the area is safe for work on the proposed underground waste disposal facility.

The decision to postpone the reprocessing plant undoubtedly will be well recieved in Washington, President Carter has been urging for two years that such plants not be built anywhere, since a byproudct of spent uranium fuel is fissionable plutonium, which when reprocessed can be used to make atomic weapons.

The West German decision, however, had nothing to do with international policy, but rather with the fact that people remain unconvinced that there are no undue risks to public safety.

Chancellor Helmut Schmidt has made it clear that he views nuclear energy as indispensable over the long run for heavily industrialized and resource-short West Germany. The chancellor favored moving ahead with the plant and also cautiously moving ahead with additional nuclear power plants.

Albrecht basically endorsed Schmidt's view of the importance of nuclear power to West Germany. But in a rare, televised speech in the state capital of Hannover, Albrecht said he could not completely guarantee the plant's security against military attack or theft of plutonium by staff workers.

He also said that while plans for the plant meet tight safety standards and probably pose no risk, the question remains whether the plant is in fact indispensable and whether the project can be supported politically.

The political question refers to deep divisions throughout West Germany on the nuclear question. These divisions will have to be healed somehow if growing public doubts are to be overcome.

Indeed, although the events today are a setback in one sense, they may well provide the public some time to calm down from the lingering effects here of the Three Mile Island accident. The decision also provides the federal government with time to come up with new and perhaps more convincing plans.

Interior Minister Gerhard Baum, in a press conference a few hours after Albrecht's address basically reaffirmed the government's intention to stick to plans for the total complex, continue pressing Albrecht and look for potential sites elsewhere.

The 10 West German federal states have considerable autonomy over internal affairs and the Lower Saxony decision is apt to prevail over federal desires.Albrecht's decision, however, was announced as an indefinite postponement, leaving open the possibility of a change in course by him or an eventual successor.

The decision spares Schmidt, at least for the time being, from a potentially devastating battle within his own Social Democratic Party where a sizable faction and the party youth wing oppose nuclear power.

Nuclear power and the issue whether new U.S.-supplied atomic weapons will be stationed on West German soil are the two questions that experienced political observers here say have the potential of critically splitting the Social Democratic Party and endangering Schmidt's otherwise powerful position.

West Germany has the fifth largest nuclear power program in the world but it has been almost stagnant for the past two years as courts and local governments have supported environmental claims and public concerns. No new plants have been authorized in those years.

West Germany has 15 nuclear power plants that now supply about 3 percent of the country's total energy consumption. Eight others under construction eventually will increase the figure to about 7.5 percent. But it was already clear before today's decision that the 1985 goal of 24 plants supplying 10 percent energy needs will not be reached.

Baum said that the state's action would not entail any automatic halt to approved new plants, although he conceded it might slow things down even further.

Atomic waste fuel from West Germany's plants is stored in part at the plants. But most - about 2,000 tons a year - is reprocessed in France at a plant at Cape La Hague.

In Lower Saxony, the Social Democrats are in opposition in government, but supported Christian Democrat Albrecht in his decision. Yet, Social Democrats in the state, as well as Baum, critized Albrecht for defending his decision on party political grounds and in effect accused him of playing politics with a vital decision.