The date of his return has yet to be determined.
Having never missed a United game through injury in over three years at the club, Mata is now expected to be sidelined for the whole of April which includes a total of nine fixtures.
Mata's absence further exacerbates a mounting injury crisis for United manager Jose Mourinho. Phil Jones and Chris Smalling were both recently ruled out after sustaining "long-term" on duty with England.
United will also be without Paul Pogba for Saturday's game against West Brom, as confirmed by Mourinho, while Zlatan Ibrahimovic and Ander Herrera are unavailable through suspension.
Despite criticising the need for international friendlies, the Portuguese insisted on Friday that his side could not allow themselves to become preoccupied with their missing stars.
"We cannot be here crying or thinking about the players who are not available to play," he said.
Mata now faces a race against the clock to recover for the final games of United's season as they battle to secure a spot in the top four.
The Spaniard will face further tests early next week, when the club's medical staff hope to determine a more accurate return date.
A spokesperson for United said: “Juan Mata has had surgery for a groin injury, further updates on his recovery will follow in due course.”