Local police responded to the allegation on Sunday and confirmed in a statement that Greenwood was in custody.
“Greater Manchester Police was made aware earlier today (Sunday 30 January) of online social media images and videos posted by a woman reporting incidents of physical violence,” said the statement.
"We can confirm a man in his 20s has since been arrested on suspicion of rape and assault", it added.
Police said the footballer remains in custody for questioning while inquiries are ongoing.
Manchester United said in a statement responding to Greenwood’s arrest: “We are aware of images and allegations circulating on social media.
"We will not make any further comment until the facts have been established. Manchester United does not condone violence of any kind."
In a second statement, the club added that Greenwood would not return to training or matches until further notice.
Related News
Eight people reported dead in crush at African Cup of Nations match
Robert Lewandowski wins The Best FIFA Men's Player award
China bans tattoos for national sports stars
Greenwood, 20, has not responded to the allegations.
Greenwood rose up through Manchester United’s academy and made his first-team debut in March 2019. He signed a four-year deal in February 2021. He has played 129 times for Manchester United and has one England cap.