The 21-year-old footballer was due to face trial in November over allegations of attempted rape, assault and controlling and coercive behaviour.
In a statement issued later on Thursday, Man United said they have launched an internal investigation with sources telling ESPN the club could only proceed with their own review once the criminal case had ended.
Sources have told ESPN that Greenwood will not play or train with United until the investigation is over and there is no timeframe for how long that might take. Greenwood last played for United more than a year ago in a 1-0 win over West Ham on Jan. 22, 2022.
United's statement read: "Manchester United notes the decision of the Crown Prosecution Service that all charges against Mason Greenwood have been dropped. The club will now conduct its own process before determining next steps. We will not make any further comment until that process is complete."
In his own statement, Greenwood said he was "relieved that this matter is now over and I would like to thank my family, loved ones and friends for their support. There will be no further comment at this time."
Explaining Thursday's announcement, the Crown Prosecution Service said key witnesses had withdrawn their involvement.
"A decision has been made to discontinue prosecution in accordance with the Code for Crown Prosecutors," a CPS statement read.
A CPS spokesperson said: "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."
The CPS added that it encouraged "any potential victims to come forward and report to police."
Chief Superintendent Michaela Kerr, Greater Manchester Police's Head of Public Protection, said: "Given the significant media coverage of this case, it is only fair that we share the news that the 21-year-old man, who had been arrested and charged in connection with an investigation opened in January 2022, no longer faces criminal proceedings in relation to this.
"The investigation team has remained in regular contact with the legal team, providing any updates of note, and so understand the rationale for the discontinuation of proceedings at this stage, and that this decision has not been taken lightly.
"Despite the media and public's interest in this case, we have decided not to comment on it in any further detail.
"I would, however, like to use this opportunity to reiterate GMP'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."
Information from Reuters contributed to that report.