Rangnick slammed Bailly for his Instagram post urging the axing of Harry Maguire.
The club's skipper, who was this week sent a bomb threat, has come under heavy fire for his poor form this term.
Bailly is desperate for more action, and he let everybody know this week on social media that he wants to partner Raphael Varane in defence.
Bailly, 28, replied to a fan who said he wanted him and the French star to start today against the Gunners.
He responded by saying “please" along with a laughing and praying emoji.
Rangnick was asked about the incident ahead of the Arsenal game, and the United chief was not happy.
He said: “If it's true what you told me, it's not the right sign and should not happen in a football club, no matter what league.
“I'm not on Instagram. Listen, I'm not talking about my players in the press conference not knowing what has happened, it doesn't make sense.
“I can only tell you, never in my life will I be part of Instagram."