Play was halted for around eight minutes after the Scotland international clashed heads with United defender Rafael in the second half of the Canaries' 4-0 defeat at Old Trafford.
Manager Chris Hughton said: "He's gone to a local hospital. I think that is very much a precaution, he was out for a period of time. It is very much concussion.
"He has also taken a whack in the incident itself so they will have a look at that and X-ray that just to make sure there is nothing broken.
"But by the time he was on his way out he was awake and aware of what was happening around him.
"Whether he will he kept in overnight or not, I don't know."
The injury to Snodgrass compounded Norwich's misery on a disappointing night.
Javier Hernandez struck twice for United, opening the scoring from the penalty spot and then doubling the advantage with a header early in the second half.
Phil Jones volleyed the third and substitute Fabio completed the scoring as the game went into 11 minutes of stoppage time.
Hughton was unhappy with the award of the penalty which led to the opening goal, which was given after the impressive Adnan Januzaj went down under a challenge from Leroy Fer.
Hughton said: "Could our performance have been better? Yes, we could have been better on the ball.
"But we were given a penalty against us which was incredibly soft and not a penalty.
"To have a penalty given against us, in that fashion, as soft as that, really gives Man United a lift and deflates you.
"But they scored good goals, they have got great quality and they are clinical in everything they do."
United have now gone six games unbeaten after a difficult start to the season and assistant boss Steve Round feels momentum is building.
He said: "This club is used to winning, it has a winning mentality.
"There were no great celebrations after the win on Saturday and none tonight.
"We just move on to Fulham, that is how it is.
"You need to go on runs in this league and this club is the best in the business at building that."
Round also praised the performance of Hernandez, who scored the winner against Stoke last weekend but is generally behind Wayne Rooney and Robin van Persie in the pecking order.
He said: "He is such a good character. I don't think it has fazed him at all.
"He is a really infectious character who loves to score goals. He has waited patiently for his opportunities and when he gets them he has taken them."