"Hector hasn't travelled... he has an inflammation of his left knee. Some ligament damage," Wenger told a news conference.
"He has to spend the afternoon in the hospital to see why he is in so much pain.
"It doesn't look a long-term problem. He tried but couldn't absorb the training session so we left him at home."
Spaniard Bellerin has featured in all 29 of Arsenal's league matches this season and has made three starts in UEFA's secondary club competition.
Arsenal are sixth in the Premier League and on a three-match losing streak, so winning the Europa League may represent their best chance of qualifying for the Champions League next season.
They face a tough challenge against in-form Milan who have won their last six matches in all competitions.
(Reporting by Shrivathsa Sridhar in Bengaluru, editing by Ed Osmond)
