On Sunday, Greenwood was detained on suspicion of rape and assault after a woman alleging incidents of violence posted pictures and videos on social media.
Police were granted extra time on Monday to question the 20-year-old and he was further arrested on suspicion of sexual assault and threats to kill.
On Wednesday, Greater Manchester Police said Greenwood was released from custody on bail pending further inquiries.
A statement said: "A 20-year-old man arrested (on Sunday 30 January 2022) on suspicion of the rape and assault of a woman has been released on bail pending further investigation".
Greenwood was suspended from playing or training with Manchester United following the weekend allegations.
The allegations were posted on Instagram on Sunday morning and included videos, photographs and a voice note which claimed to be a conversation between Greenwood and the woman. They have since been deleted.
Complainants of sexual offences must not be identified and their anonymity is protected for life under the law.
Greenwood made his debut in 2019 and has since made 129 appearances for Manchester United. He made his senior England debut in 2020.
On Tuesday night, Manchester United released a statement reiterating their "strong condemnation of violence of any kind".
The club added: "As previously communicated, Mason Greenwood will not train with, or play for, the club until further notice."
The striker, from Bradford, was earlier removed from versions of the FIFA 22 game following his initial arrest after Nike suspended their deal with the player.
A spokesperson from the game's manufacturer Electronic Arts said: "Mason Greenwood has been removed from active squads in FIFA 22 and has also been suspended from appearing in FIFA Ultimate Team (FUT) packs and Ultimate Draft."
An earlier Nike statement read: "We are deeply concerned by the disturbing allegations and will continue to closely monitor the situation."
Manchester United are allowing supporters who have purchased shirts with Greenwood's name printed on them to change them for another shirt and name of their choice.
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