On 20 December 2010, Cohen was seriously injured in a motorcycle crash. He was taken to Tel Aviv's Ichilov Hospital, where he was immediately taken into surgery. On 28 December 2010, the hospital declared that Cohen was brain dead. His brain death was confirmed by his son Tamir later the same day. Paying tribute to Cohen, Kenny Dalglish said "Avi was a lovely man who will be remembered fondly by everyone at Liverpool who knew him. He quickly integrated himself into the football club when he joined us and spent a lot of time learning English which really made him popular. He was well liked by all the lads and although he didn't spend a long time at the club, he certainly left his mark and no-one will forget how he helped us win the league against Aston Villa. My thoughts and those of everyone connected to the club are with Avi's family." Ally McCoist said "we knew his situation was bad but never for a second did we think it would come to this" before going on to say it was "so sad to hear that he has passed away."