The Austrian Bundesliga's decision has left Admira, previously bottom of the 10-team table with eight points and already on to their third coach of the season, with no points from their 11 games.
Admira were "fully unprepared" for the decision and would appeal, the club said on their website (www.admirawacker.at). They blamed the move on a long-running and complex dispute over where they should be paying their local taxes.
Polster was followed by his assistant Oliver Lederer, who was in charge for a month but had to step aside because he lacked an official coaching license.
He was officially replaced in September by Walter Knaller, although the club says that the pair are joint coaches.
Admira Wacker are the product of a number of fusions over the years, typical of the often bewildering changes in Austrian football.
The most recent merger was in 1997 when Admira Wacker joined forces with VfB Moedling, which was founded in 1911.
Admira Wacker had been created in 1971 by the a merger of Wacker Vienna and Admira Vienna, who themselves had been one of Austria's most successful clubs until that point with eight league and six Cup titles.