The Afghan later admitted uploading the image, saying it had been a joke.
He is to face charges of making threats to commit crime.
His accommodation was searched but investigators found nothing to suggest the threat was real, police said in a statement.
Last year a Tunisian asylum seeker drove a lorry at people visiting a Christmas market in Berlin, killing 12 and injuring 49.
In October an investigation into the attack revealed mistakes by German police and security services.
It said police missed several chances to arrest and deport attacker Anis Amri, who fled Berlin after the attack but was later shot dead by police in Italy.
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