Germany was offering up to €100,000 ($104,000) for information leading to the arrest of the Tunisian suspect.
Milan police shot dead the Tunisian man suspected of carrying out Monday's truck attack on a Christmas market in Berlin, Italy's Interior Minister Marco Minniti announced on Friday.
The 24-year-old Anis Amri is believed to be behind the attack which killed 12 people and wounded 49 others. Daesh released a video purportedly that shows Amri pledging allegiance to the terrorist group.
Minniti said Amri was fatally shot around 0200 GMT after firing at two policemen who had stopped his car for a routine identity check.
Amri shot one policeman in the shoulder during the exchange. He is recovering in hospital.
Italy had Amri's fingerprints on record because he served a term in prison in Sicily between 2011 and 2015 for starting a fire in a refugee centre.