It happened in Nauen, a town which has seen repeated far-right protests against the arrival of asylum-seekers.
It's not the first time fire has destroyed premises designated to provide shelter to hundreds refugees.
In the first half of this year alone, about 150 arson or other attacks have been carried out on refugee shelters.
German Interior Minister Thomas de Maizière says such violence does not represent the views of most Germans.
"We are outraged about the attacks which happened, and are still happening, on asylum-seekers and asylum-seekers' homes. But those who are doing this are not a majority. They are not what characterises Germany."
It comes just days after protests at an asylum shelter in the eastern town of Heidenau turned violent.
Dozens of police officers were injured in the clashes, which German Chancellor Angela Merkel has described as abhorrent and shameful.
Members of the Social Democrat Party have also been targeted after expressing support for the migrants.
The party's Secretary General, Yasmin Fahimi, says the party's headquarters in Berlin had to be evacuated because of a bomb threat.
"It is meant as an attack against our constitution and our democracy. For us at the SPD, we will not give a single millimetre to our position."
Germany takes in the largest number of refugees in Europe and expects up to 800,000 people will have sought asylum by the end this year.
Many make the perilous journey across the Mediterranean by boat, fleeing conflicts in Africa and the Middle East.
A Somali woman, who gave birth on a German navy ship, was among the 4,000 people rescued in the Mediterranean Sea over the weekend.
The ship's surgeon, Marius S, assisted with the birth.
"Of course, on board a warship this is not an everyday emergency. We knew that the pregnant woman was very weakened by the long and gruelling journey from Somalia, so the evening before we gave her preventive medical attention."
The mother and baby are said to be doing well.
Meanwhile, a United Nations expert on migrant rights has called on European leaders to avoid using language which demonises migrants.
The UN special rapporteur on the human rights of migrants, Francois Crepeau, has issued this statement:
"Building fences, using tear gas and other forms of violence against migrants and asylum-seekers, detention, withholding access to basics such as shelter, food or water and using threatening language or hateful speech will not stop migrants from coming, or trying to come, to Europe."
He's called on European countries to open official channels and their labour markets to migrants.
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