The measure followed a ban on gatherings of more than 1,000 people issued by the Bavarian government on Tuesday in response to the spread of coronavirus.
The game is one of several high-profile fixtures in Germany to be played without fans in the coming weeks, including Saturday's Ruhr derby between Borussia Dortmund and Schalke, and Bayern Munich's Champions League clash with Chelsea next week.
Wednesday's Rhine derby between Borussia Mönchengladbach and Cologne will be the first game in Bundesliga history to be played without fans.
Bundesliga fixtures had been going ahead as usual, even as the number of people testing positive for the coronavirus continued to rise in Germany, passing 1,000 on Monday.
Yet on Sunday, the country's Health Minister Jens Spahn requested that all events with more than 1,000 people be cancelled “until further notice”.
The decision to close stadium doors will ultimately be made on a case-by-case basis by regional authorities.
The state of North-Rhine Westphalia, where both the Rhine and Ruhr derbies take place, has been Germany's worst hit region, with nearly half of all coronavirus cases.
Authorities have also moved to prevent events exceeding 1,000 people in other states, such as Bremen and Bavaria.
On Wednesday it was announced that the Bundesliga match between Union Berlin and Bayern Munich on Saturday will be played behind closed doors because of the coronavirus scare.
“The match will be played without spectators,” the city deputy health chief Dilek Kalayci told Spreeradio station despite Union Berlin's statement Tuesday saying the match would be open to an expected 22,000 fans.
German Football League (DFL) chief Christian Seifert warned Sunday that “the season must end by mid-May” in order to ensure clarity over promotion, relegation and qualification for international competition.