Rashford will have the operation "imminently" and is expected to be out until October.
A club statement on Friday read: "Following consultation between Marcus, the manager, club medical staff and a specialists, Marcus will undergo surgery imminently to resolve his shoulder injury.
"He will now focus on his rehabilitation in order to return as soon as possible."
Rashford played through the pain last season, carrying both shoulder and foot problems for the majority of the campaign.
Rashford wrote later in the day on Twitter: "I've read some call me selfish for holding off getting the surgery this season but it was never about putting myself first and that's how we've reached this point, and as a 23-year-old I have had to learn the hard way.
"To guarantee I can play this game as long as possible, I need to listen to my body. Everyone has an opinion but no one knows my body better than me.
"When I step on the pitch I always give 100%. Physically my 100% just wasn't possible. I'm walking away from last season with 36 goal contributions, but more importantly I'm walking away with lessons learnt."
After returning from holiday after the tournament, Rashford held talks with Ole Gunnar Solskjaer and club staff before deciding to have surgery.
Anthony Martial is also due back in training as he steps up his recovery from a knee injury that saw the Frenchman miss the end of last season.