United's top scorer for the campaign was forced off during the midweek Emirates FA Cup win over Wolves, having entered the fray in the second half as a substitute.
The manager confirmed Rashford hurt his back and said the forward would probably not be fit until February.
“He got a couple of knocks and jolts when he came on against Wolves and aggravated his back,”
Ole told MUTV and Sky Sports.
“He's had some trouble before and we're going to give him time to recover and rest before we put him back on the pitch.