The Brazilian full-back, 24, suffered the injury in the lead-up to United's 3-2 win over Roma at the International Champions Cup (ICC) on Saturday.
While the extent of the injury remains unknown, Rafael will head back to the UK, the Premier League giants confirmed on Monday.
"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.
