There were no injuries reported in the evacuation or demolition of the package, which authorities said did not appear to include a fuse or other parts for a detonation.
Center of Potsdam evacuated after suspicious package found.
A controlled explosion was carried out on the suspicious package.
Brandenburg state Interior Minister Karl-Heinz Schröter told reporters a powder found in the device is undergoing tests to determine whether it was explosive. He said it is not clear whether the package was a real weapon.
Police warn that there may be more such packages in the area.More news: Netflix Renews Drama 'Mindhunter'
Both the market and the surrounding area have been evacuated as special forces investigate.
In that case, a Tunisian man hijacked a truck and drove it into a crowded market, killing 12 people in an attack that was later claimed by the Islamic State group.
Police are beefing up their presence at Christmas markets across Germany.
The Brandenburg Police Department, which covers Potsdam, posted a tweet saying the device was an IED.
A temporary memorial to the victims of last year's attack is set to be replaced by a permanent one on December 19, at the historic Kaiser Wilhelm Memorial Church on the site of the market that was attacked. It lies about 40 kilometers southwest of Berlin.