The United left-back sustained a hamstring injury and was substituted 36 minutes into the 4-0 home win against West Brom on Saturday evening.
Evra did light training on Monday morning but the French international defender has not recovered in time for the match against Celtic at Old Trafford on Tuesday evening although he should be fit for United's next match against Everton at the weekend.
"It's too big a risk with a hamstring injury," manager Sir Alex Ferguson has said.
"He should be OK for Saturday."