A spokesman said Berlin had not yet received "official confirmation" from Italy that the dead man was in fact the suspect.
"There are growing signs that this is actually the person (wanted in the attack). Should this be proved true, the ministry is relieved that this person no longer poses a danger," interior ministry spokesman, Tobias Plate, told reporters.
Foreign ministry spokesman Martin Schaefer said Berlin was "grateful to the Italian authorities for the very close cooperation based on trust".
"Our colleagues at the consulate in Milan were informed in a very timely way," he told the same news briefing.
Plate said that Berlin had not yet received "official confirmation" from Italy that the dead man was in fact the suspect, Anis Amri, after Italy's interior minister Marco Minniti told a news conference in Rome that Amri had been shot after firing at two police officers.
A spokeswoman for Chancellor Angela Merkel, Ulrike Demmer, declined to comment until the written confirmation had arrived from Rome.
"I ask you for a bit of patience," she said.