The Republic of Ireland midfielder is suspended for Saturday's encounter at Parkhead after passing the disciplinary points threshold and will be joined in the stands by defender Darren O'Dea, who is also banned after picking up a yellow card against Aberdeen last week.
While right-back Andreas Hinkel is back after recovering from a thigh injury, the Hoops will again be without experienced defenders Glenn Loovens and Jos Hooiveld, who are both carrying hamstring injuries, which will mean another reshuffle to the Hoops' rearguard, with fringe full-backs Mark Wilson and Lee Naylor in contention for a place in central defence.
Celtic remain 10 points behind Old Firm rivals Rangers and the Parkhead boss will have to do without the man who has arguably been his best performer this season.
"Good players win you football matches, good players make the difference and Aiden McGeady fits into that category," Mowbray said.
"It is one less string to our bow but we have other good players waiting for an opportunity.
"Let's hope the guy who comes in to fill his boots does the job and makes it difficult to pick the team for the next game."
United boss Peter Houston revealed he will send his Dundee United players out to go for Celtic's jugular - because that's the only way they know how to play.
He said: "We're going to go there and have a right go at Celtic.
"Obviously we'll have to make sure we keep the door shut at the other end but I always feel we'll create chances against anyone.
"It's the only way we know how to play so why tinker with it?
"The best way for Dundee United to play is by attacking. When we sit in and hold, we're not as good, so I'm not planning to change it.
"There's no way we'll sit and defend for 90 minutes because that just invites trouble.
"You can't tell the likes of Danny Swanson, Morgaro Gomis and Craig Conway to sit behind the ball so I don't see any point.
"We'll go there, be positive and attack them as much as we can.
"We've got to be brave, pass the ball and take our chances when they come along.
"If we do that, then I think we can get a result."
Celtic 4/11, Draw 7/2, Dundee Utd 17/2