The 21-year-old was arrested in January last year amid allegations surrounding images and videos that emerged online.
He was later charged with attempted rape, controlling and coercive behaviour and assault occasioning actual bodily harm.
The Crown Prosecution Service said the charges were discontinued after key witnesses withdrew their involvement.
A spokesman said: “We have a duty to keep cases under continuous review.
“In this case a combination of the withdrawal of key witnesses and new material that came to light meant there was no longer a realistic prospect of conviction. In these circumstances, we are under a duty to stop the case.
“We have explained our decision to all parties.
“We would always encourage any potential victims to come forward and report to police and we will prosecute wherever our legal test is met.”
Within hours of the allegations surfacing online at the beginning of 2022, the forward, who has made one appearance for England, was suspended from playing or training with the Old Trafford club.
The club has been asked by the BBC to comment.
Greater Manchester Police said it was “only fair” to announce Greenwood would no longer face criminal proceedings.
Ch Supt Michaela Kerr said the decision had “not been taken lightly”.
She added: “I would, however, like to use this opportunity to reiterate the force's commitment to investigating allegations of violence against women and girls and supporting those affected, regardless of their circumstances, throughout what can be a hard and upsetting time for them.”