Louis van Gaal confirmed the striker's injury, which he suffered in the 1-1 draw at Leicester, was worse than feared.
The 30-year-old, who has played 499 games for the club, will miss Saturday's home game against West Ham and the crucial Champions League fixture in Wolfsburg next Tuesday.
"It's a nasty injury
He shall not play his 500th game (on Saturday) because he is more injured than I thought so we have to wait for that game," the United manager said.
"His ankle is not good enough and we have to recover that ankle with a lot of strength
He has to do a lot of exercises to make his ankle stronger
He needs more time."
Van Gaal later confirmed Rooney would also miss Tuesday's game in Wolfsburg, which United need to win to guarantee their place in the knockout stages of the Champions League.
When asked if Rooney would miss the match at Wolfsburg, Van Gaal said: "Yes, I think so."
Van Gaal also confirmed defender Marcos Rojo would be sidelined for a number of weeks after dislocating his shoulder in training.
The Argentina left-back suffered the same problem last November in the 1-0 defeat at Manchester City and had only just returned to training following another injury.
"He was recovered of his (previous) injury so he trained with us on Wednesday after we gave all the players two days off," Van Gaal said.
"He started fresh with us but he fell down and it was a bad fall and he dislocated his shoulder.
"It's more or less the same as what happened last season (at City) so he is for more weeks out.
"Whether he shall be operated on is a question for Marcos and the doctor
We have to wait for the scan
We have to make the scan at the proper time."
Source : PA
Source: PA