That means he will not be available for the Toffees' remaining games against Southampton, Manchester City and Hull.
Everton reported the news on their website, saying: "Roberto Martinez today revealed that the Belgian has a small tear in his groin and will be out for the next three weeks."
Mirallas has scored eight goals for Everton this season, including three in the last four games.
He netted the second goal against United on Sunday, scoring from a tight angle after beating the offside trap.
Everton trail Arsenal by a point in the race for fourth place as they bid to finish in the top four for only the second time in the Premier League era.
Martinez will hope for better news to come on the injury front, with captain Phil Jagielka, Steven Pienaar and Darron Gibson all in line to return before the end of the season.
- Sports & Recreation
- Manchester United
- groin injury