The seven-time winners of Europe's premier club competition already had Ignazio Abate, Mattia De Sciglio, Matias Silvestre, Daniele Bonera and Giampaolo Pazzini sidelined prior to their 2-2 draw with Torino.
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To make matters worse, Stephan El Shaarawy was forced to pull out of that game with a thigh problem, Riccardo Montolivo was withdrawn from the action with a similar injury and Kaka around faces a month out with a thigh strain.
Although the Rossoneri will be down to the bare bones for the Celtic clash, coach Massimiliano Allegri told the club's official website: "We'll make do with who we have and we'll have fresh players ready to play what is a delicate and important game."
Allegri's men have won just one of their first three games in Serie A and only salvaged a point at Torino courtesy of late goals from Sulley Muntari and Mario Balotelli.
A similarly slow start in European competition could well prove costly as Milan have been drawn in a difficult Group H that also features Barcelona and Ajax.
Celtic will be aiming to follow up last season's impressive showing in the Champions League, which was highlighted by a shock 2-1 home victory over Barcelona.
Victor Wanyama scored the opening goal of that game but he has since departed to Southampton, while star striker Gary Hooper also left the club this summer to join Norwich City.
One of Celtic's summer additions, full-back Steven Mouyokolo, is set to miss the entire group stage after rupturing his Achilles tendon in training, while winger James Forrest returned from international duty with Scotland nursing a back complaint.
However, former Ajax winger Derk Boerrigter, defender Virgil van Dijk and forwards Teemu Pukki and Amido Balde could all make their first Champions League appearances for Neil Lennon's side.
Midfielder Nir Biton missed Saturday's 3-1 win at Hearts due to work permit issues and it is unclear whether he will be eligible to feature against Milan.
Pukki - a deadline-day arrival from Schalke - made an immediate impression on his debut against Hearts, coming off the bench to head home the final goal.
"It is a big thing for me to play again in the Champions League," said the Finn. "Last year I also played with Schalke but not as a starting player so I'm hoping to play a lot of games in the Champions League."