The Hoops winger missed the Scottish Premiership win over Hearts at Tynecastle on Saturday with an ongoing sciatica problem but has also taken ill and was absent when the Hoops squad met up at Glasgow airport this morning ahead of their flight to Italy for the opening Group H fixture.
Midfielder Joe Ledley has a groin problem but checked in with the rest of the Hoops squad as did fellow Wales international Adam Matthews, who hobbled off against the Jambos with an ankle injury.
New signing Nir Biton will meet up with his new team-mates in Milan but the Israel midfielder is unlikely to feature.
Celtic assistant Johan Mjallby said: "Unfortunately James is ill.
"He has been feeling that sciatica problem lately but at the same time he is ill.
"It is brilliant that Joe is here. When I left the training ground he was struggling and we were pretty sure that he would not be able to make it so that is great news.
"The scan has come back and obviously shown that he has a chance."
Reports from Italy claimed that AC Milan boss Massimiliano Allegri has lost five top-team starters, including skipper Riccardo Montolivo and new signing Kaka, with four other injury victims leaving his men nine men short.
However, Mjallby said: "I am not going to be fooled by that. AC Milan is always going to be a very difficult task.
"They have a lot of quality players, they are a strong team and we have to be at our best to get something from the game"