Their statement said: “The executor of the operation in Berlin is a soldier of the Islamic state and he executed the operation in response to calls to target nationals of the coalition countries.”
They claimed responsibility in their Amaq news agency, around 24 hours after a truck ploughed through a Christmas market in the capital.
The attack killed 12 people and injured around 50 others.
German authorities have still not confirmed the incident was a deliberate attack.
A man who was arrested in the immediate aftermath of the crash has since been released.