Sweden's pop supergroup, Abba, is facing its Waterloo - a threatened Socialist takeover.

In the run-up to a general election Sept. 19, the musical group, which numbers its fans in millions all over the world, is fighting a last-ditch stand to keep the financial empire it has built up in its homeland. Abba's riches flow , appropriately, from such hits as ''Money, Money, Money'' and ''Winner Takes It All.''

A proposal that would allow the trade unions to take over private industry is one of the main planks of the Swedish Social Democratic Party's election manifesto.

Abba, which runs several of Sweden's most profitable companies, is a prime target for the Socialist program masterminded by Marxist economists of the Swedish Confederation of Trade Unions, which is affiliated to the party in much the same way as the Trades Union Congress is linked to the British Labour Party.

The plan allows for the establishment of 13 so-called wage-earner funds. Successful companies would be forced to contribute 20 percent of what the unions describe as ''excess profits'' to the funds. Workers would also contribute with enforced deductions from their wages.

With this cash, the union-run funds would then buy shares in all leading companies.

Per-Martin Meyerson, leading economist with the Federation of Swedish Industry, estimates that within five years the funds would control most of Swedish industry. ''The market economy would cease to exist,'' he told the Monitor.

Olof Palme, leader of the Swedish Social Democrats, who have swung steadily further left in recent years, says the funds are necessary to raise investment for industry and haul Sweden out of an economic crisis of horrifying dimensions.

The foreign debt is increasing at the rate of $300,000 every hour or by almost $3 billion a year, the borrowing made necessary to prop up a public sector that employs one-third of the working population of 4.5 million people.

Since 1976, when the Social Democrats lost power after 44 years in office, Sweden has been ruled by a succession of weak, non-Socialist coalitions that have failed to come to grips with economic problems.

Unemployment is rising. The official figure is only 3 percent of the work force. The reality is grimmer. Thousands of people have subsidized jobs or attend government retraining programs with little hope of finding work afterward. This ''concealed unemployment,'' as it is known here, is financed by the money borrowed abroad at high interest rates.

Swedish aid to the third world is still meeting the United Nations' aim of 1 percent of gross national product.

Many of Sweden's 6 million voters are not content with the government's performance and are disenchanted with current Prime Minister Thorbjorn Falldin, who his critics think is more at home on his sheep farm in the far north than in the corridors of power in Stockholm.

The Social Democrats have a commanding lead in all public opinion polls. If they win, it could be the beginning of the end for Abba.

The group's manager, Stig Anderson, is deeply concerned by the threat of a Socialist takeover of his empire.

''If we had had these funds today, we would have been forced this year to part with about $2.16 million,'' he said. ''Why should I continue to work 14-15 hours a day to give money away like this?

''The funds are just a device so that the unions can get power. They would be disastrous for the country. It is ridiculous to think that they could take care of the money better than us professionals.''

Not only could Abba lose its financial empire, whose total turnover is more than $200 million and extends into a wide range of Swedish industry, but the four group members may be driven from their beloved homeland if the Socialists come to power.

''We don't want to leave Sweden,'' said Anderson sadly. ''Our roots are here. We have our friends here. I intend to stay here and fight these funds even if the Social Democrats are elected. But if it becomes impossible, of course it would be very easy for us to move out.

''We get hundreds of requests from British and American artists asking us to produce them. We could establish production companies in London, Los Angeles, or New York. I have personally had inquiries from very big companies in Britain and the United States asking me if I would like to take care of their affairs.''

Anderson is currently organizing a gala concert at Grona Lund, Stockholm's open-air amusement park, on Sept. 5, to help finance the fight against the Socialist takeover.

And Bjorn Ulvaeus, who has composed many of Abba's greatest hits, is now penning a leaflet alerting young people to the dangers of the funds.

''We are trying to reach young families,'' said Anderson, ''It is their children's futures that are at stake. This election is tremendously important. Someone said to me the other day that it might be the first time that a country will freely vote to go behind the Iron Curtain. Unfortunately, that could be the truth of it.''