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 this weekend's home game against West Ham and the crucial Champions League fixture in Wolfsburg next week.
"It's a nasty injury. He shall not play his 500th game (on Sunday) because he is more injured than I thought so we have to wait for that game," the United manager said.
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"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 the Champions League game in Wolfsburg, which United need to win to guarantee their place in the knockout stage.
