Vidic suffered the injury after colliding with his goalkeeper David de Gea's knee, and remained on the ground for a number of minutes. When he got up, he was led down the tunnel, holding his head, and was replaced by Tom Cleverley at the start of the second half.
Speaking after the match, United manager David Moyes confirmed the 32-year-old was conscious after the incident but "will get a scan and as far as we know he is ok".
"I've had the chance to look at it again it's a terrible sort of clash. It's an accident, and hopefully he'll be ok," he said. "I'll find out more from the medics later on."
A United statement, released on Monday, said: "Nemanja Vidic has been released from hospital after suffering concussion."
Vidic is not due to play again until Nov. 24, when United travel to Cardiff in the Premier League. However, no timescale has been put on his return to training.
Information from the Press Association was used in this report.