Vidic left the field shortly before half-time after colliding with team-mate David de Gea.
The Serbian was clearly dazed and was sent to hospital for examination by the club before later returning home.
"Nemanja Vidic has been released from hospital after suffering concussion," said a United statement.
Vidic is not due to play again until November 24, when United visit Cardiff in the Premier League.
However, no timescale has been put on the 32-year-old's return to training.
While there is no mandatory period for Vidic to rest, United's medical staff will need to be satisfied the defender has fully recovered before he is allowed back on the pitch.
- Sports & Recreation