The Serbian looked shaken after a collision with his goalkeeper David de Gea just before half-time at Old Trafford.
The defender did not need a stretcher but was led down the tunnel and did not return for the second-half.
United boss David Moyes told Sky Sports: "He has gone to hospital, I have only just seen him myself and I didn't see how bad it was from the touchline, but it was a terrible clash. It was an accident but hopefully he will be okay, I will find out more from the medics later on."
The incident occurred just minutes after Arsenal keeper Wojciech Szczesny required treatment after a clash of heads with United's Phil Jones.
Szczesny did not immediately move after hitting the ground following the aerial collision but he quickly recovered after being treated by the physio and played on.
The incidents came a week after Tottenham keeper Hugo Lloris played on after briefly being knocked unconscious at Everton last week.
The player insisted he was fit to continue on that occasion and manager Andre Villas-Boas decided to keep him on.
That decision was widely condemned by medical experts including FIFA's medical chief, and led to calls for stricter protocols for incidents of concussion on the field.
Headway, the head injury charity, was highly critical of Spurs but said it was too early to say whether Arsenal had made the right call on Szczesny.
Headway spokesman Luke Griggs said: "I don't want to get involved in judging the decision of Szczesny - every situation is unique and different and the medical team have made a call.
"With Vidic, they have taken him off after the medical team deemed him not fit to continue. He was unsteady on his feet, there were more obvious signs.
"From the very start the whole situation was to raise awareness about head injuries.
"It has made people think. Especially the impact it has on youth and amateur football, about taking risks when they are playing football. They might want to be a hero and carry on - and they don't have medical teams at amateur football.
"If they are unsure and unsteady on their feet, it is best to go off."