The striker was able to play a part in England’s run to the Euro 2020 final despite struggling with the injury throughout last season.
He will now have surgery and could be out for as long as three months.
“Following consultation between Marcus, the manager, club medical staff and specialists, Marcus will undergo surgery imminently to resolve his shoulder injury,” United said in a statement.
“He will now focus on his rehabilitation in order to return as soon as possible.”
Ole Gunnar Solskjaer;s side will be looking to improve on last season’s second-place league finish and start their season on 14 August against Leeds United at Old Trafford.
They have a replacement at hand after they signed Rashford’s England team-mate Jadon Sancho from Borussia Dortmund this month for £73m.