The Brazilian full-back, 24, picked up the injury in the lead-up to United's 3-2 win over Roma in the International Champions Cup on Saturday.
Though the extent of the problem remains unknown, it will come as a blow to manager Louis van Gaal, who will implement a wing-back system at Old Trafford next season and is short on defensive options.
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The Dutchman is in the market for reinforcements following the departures of Rio Ferdinand, Nemanja Vidic and Patrice Evra, as well as the necessity of playing three central defenders in his 3-4-1-2 formation.
Rafael had been expected to take a right-sided wing-back role, with Antonio Valencia providing competition for places given the lack of a second-choice right-back.
Phil Jones and Chris Smalling had provided cover for the Brazilian last season, but they are currently two of the club's only three senior centre-backs.
Rafael will undergo treatment at the club's training base with a view to rejoining his team mates later in the summer.
"Rafael has returned to Manchester to continue treatment on the groin injury sustained in training in Denver," a statement published on the club's official website read.
"As he was unlikely to participate in the remaining tour games, returning to the Aon Training Complex affords the best overall option for his recovery in time to continue pre-season preparation when the team returns."
United have scheduled matches against Inter and Real Madrid at the ICC before a clash against Valencia at Old Trafford on August 12.
Louis van Gaal's men open their Premier League campaign at home to Swansea City four days later.