The Spain international had played every minute of the Gunners' Premier League campaign until he was not included in the starting line-up for Monday's (AEDT) 2-1 Premier League defeat to Brighton and Hove Albion.
Wenger said that Bellerin will not return for the first leg of the UEFA Europa League Round of 16 tie with AC Milan, although he does not fear the problem is long term.
"No, he is injured," Wenger said when asked if Bellerin would feature at San Siro on Friday (AEDT).
"He has an inflammation of his left knee. Some ligament damage. He had to spend the afternoon in the hospital to see why he is in so much pain.
"It's not a long-term thing."
Arsenal will also be without Nacho Monreal and Alexandre Lacazette against Milan, although it has no other injury worries.
"For team news, apart from that, of course Lacazette is not ready and we had to leave Monreal behind as well because he's not ready," Wenger said.
"He started a little session but he's not ready."
Arsenal is looking to end a run of four consecutive defeats in all competitions, its worst sequence since October 2002.