Vidic left the field shortly before half-time at Old Trafford following an accidental clash with United goalkeeper David de Gea.
The Serbia central defender, clearly dazed, was sent to hospital for an examination.
"Nemanja Vidic has been released from hospital after suffering concussion," a United statement issued Monday confirmed.
Vidic is not due to play again until 24 November, when United visit Cardiff in the Premier League, although no timescale has been put on the 32-year-old's possible return to training.
In Vidic's absence, champions United completed a 1-0 win at home to Arsenal that saw them move to within five points of the Premier League leaders.