Security was increased at the newly-opened centre near Dresden at the weekend after two nights of protests.
Left-wing activists staging counter-demonstrations have clashed with the right-wing protesters.
Germany says it expects up to 800,000 people to seek asylum by the end of 2015.
German news magazine Der Spiegel reports that the violence on Friday night followed a demonstration earlier in the evening, called for by a Facebook group linked to the far-right NPD party.
The group later distanced itself from the violence that followed.
More about:
