It has also been revealed that Glenn Loovens will also miss the game due to torn quadriceps.
Naka said "My left thigh is aching. I can't even stand up without holding on to something at the moment.
"I want as much time as possible to recover so I can give myself every chance of playing against Manchester United but I don't think I will be able to play on Sunday.
"I'm in a lot of pain right now, so we can only wait and see how I improve.
"I complained to the referee because he should have protected me and the other Celtic players from the bad fouls which were being committed by their players."
Loovens said: "They have said I will be back in two weeks.
The problem is the thigh.
"It's hard to tell just how long I'll be out and you just have to go day by day. But two weeks is what the doctors have told me."
We really are going through a testing time with injuries. The recent two additions join the long list of McManus, Crosas, Samaras and JVH who are all doubtful for the visit of Man Utd. Thankfully we still have cover for Naka in that McGeady, Maloney or Robson can all cover his flank and Darren O'Dea has proven in the past that he is more than capable of playing in the Champions League.
Yours in Celtic
Clydebuilt