United say they will not seek an immediate replacement.
The club said in a statement: "Manchester United can confirm that first-team coach Eric Ramsay will depart the club to join Major League Soccer team Minnesota United as head coach.
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"Eric, who will remain in his current role until after our game against Manchester City on Sunday, has been part of our first-team coaching group since joining from Chelsea in 2021.
"His responsibilities will be shared across the rest of the coaching team for the remainder of the season.
"We would like to thank Eric for his contribution, and wish him the best of luck in the US in his first head-coach role."