A 150-strong group of demonstrators lay down and blocked a street until local government leader Christoph Hillenbrand agreed to house them in the tents, Spiegel reported.
The protest occurred just hours before Munich mayor Dieter Reiter was due to visit the refugee centre.
Social Democratic Party (SPD) councilwoman Julia Schönfeld-Knorr told Bayerische Rundfunk that the tents were only a temporary solution for around five days until more permanent accommodation could be found.
“Tent accommodation is OK for the moment, but not if it gets any colder,” a spokeswoman for the Munich Youth Ring that manages the tents told the Sueddeutsche Zeitung.
With between two and three hundred people arriving every day, the Bayernkaserne, a former barracks which has become the main accommodation centre for asylum seekers, is over capacity.
Around 100 people have been sleeping outside on cardboard boxes.
Thursday's protest was sparked off when a mother with a young baby was allowed to move into a hotel room with its own bathroom.
The police maintained their distance from the protestors and prevented traffic from entering the road while local government representatives negotiated with the asylum seekers.
Munich is the point at which two routes taken by many refugees fleeing to Germany end: one from North Africa via Italy, and the other from the Middle East through Greece and the Balkans.
Over 8,000 asylum seekers were in Munich accommodation in August 2014, the latest government figures show.
And a similar number of people had to be sent to centres scattered around the rest of Bavaria and Germany.
Refugees are divided up between the German federal states (Bundesländer) according to the “Königstein system”, which allocates the greatest number to the most populous states.
But the system is creaking under the strain, especially due to delays in offering the refugees the medical examinations required by law.
High numbers of refugees have become a political football in recent weeks, with Interior Minister Thomas de Maiziere saying that other EU countries should take some of the load, while others say that Germany can do more.
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