The 24-year-old was left out of Steve Clarke’s national team squad for next month's World Cup qualifiers against Denmark, Moldova and Austria.
McTominay played in all three games at the Euros, including a starring role at centre-back in the 0-0 draw with England at Wembley.
His club provided an update on his fitness on Thursday.
A statement on the club's official website read: "Scott has undergone surgery for an ongoing groin injury that was causing significant pain when playing.
"Having tried all other treatment options in pre-season, surgery was deemed necessary to resolve the issue. We hope to have him back soon."
McTominay started United's opening match of the season against Leeds United but was restricted to a cameo role in their 1-1 draw at Southampton last time out.
The midfielder expressed his frustration at missing the upcoming Premier League clash against Wolves and Scotland duty, but promised supporters that he would be back sooner rather than later.
He said on Instagram: "Just to let you all know I've had minor surgery on an issue which has needed managing for the last couple of months.
"I hate missing games so to be missing Wolves on the weekend and the international break is so disappointing but that's part and parcel of the game. Wishing all the boys the best of luck and I will be back sooner than you think."