It's expected the striker will be out of action for up to three months.
Rashford is optimistic he will play again before the end of October but could miss United's first 11 games of the season in the Premier League and Champions League as well as England next five World Cup qualifiers.
The decision to have an operation was made following talks between Rashford and manager Ole Gunnar Solskjaer this week before the player was due to report for pre-season training on Sunday, says the Daily Mail.
The 23-year-old striker was strongly in favour of surgery after struggling since November with a muscle tear in his left shoulder.
United were hoping that a three-week break after Euro 2020 would ease the problem, but Rashford returned from a holiday with the club's new £73million signing Jadon Sancho and friends in the Turks and Caicos Islands feeling that an operation was still the best course of action.
Rashford had a scan on the shoulder in Liverpool a fortnight ago which revealed that the muscle tear is unlikely to get any worse. However, he wanted the problem cured once and for all after requiring painkilling injections to play last season.
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