The suspect was killed in a shootout in Sesto San Giovanni -- a town near Milan -- just after 3am local time, say Italian police in their Twitter feed.
When the man was asked for his papers, he pulled a .22 calibre gun out of his backpack and fired, continued the tweet.
The driver of the police car returned fire, killing the suspect. A policeman was injured in the shootout and is in hospital, according to Italian police.
Twelve people were killed and dozens injured when a truck plowed into the busy Berlin market Monday.
Developing story by CNN - more to come