The 20-year-old was also arrested on suspicion of assault on Sunday following allegations on social media.
He was then further arrested on suspicion of sexual assault and making threats to kill on Tuesday.
Manchester United previously said the forward would not return to training or matches until further notice.
Greater Manchester Police said Greenwood was arrested after the force “became aware of online social media images and videos posted by a woman reporting incidents of physical violence”.
It said magistrates had granted a second extension to keep him in custody until Wednesday but he had now been bailed pending further investigations.