Snodgrass suffered the injury after a clash of heads with Manchester United defender Rafael in the Canaries' 4-0 Capital One Cup defeat at Old Trafford.
The Scotland winger received on-pitch treatment after suffering a blow to his eye socket and was taken to hospital as a precautionary measure.
He was released hours later although Norwich's official website confirmed that he will be checked over before a decision is taken on whether he will feature in Saturday's Barclays Premier League visit to Manchester City.
Manager Chris Hughton said: "We have a tight squad as it is and we need to make sure as many as possible are okay for the weekend, because of course we lost Alex Tettey in the last game too.
"Unfortunately for us we've picked up a few injuries this week, but it's one we've got to work around."