The 27-year-old sustained the problem during United's 2-0 victory over Norwich City on Saturday afternoon.
Has has since admitted that he should have come off during the match at Old Trafford, but hopes that the injury will not keep him sidelined for too long.
"I got a stamp on my ankle at the start of the match and should perhaps have come off, but it was not an option in my mind," he said.
"I chose to carry on and pay the price. And although I have to sit on the couch with my leg up now, it was incredibly important to me to play.
"The medical staff at United believe that the earliest I could train again is next week."
Lindegaard's appearance against the Canaries was his first in the Premier League this season.