The Canaries midfielder went down in the 56th minute of the Capital One Cup fourth-round tie after a clash of heads with Rafael, and was eventually substituted after receiving nine minutes of treatment in the penalty area.
And Hughton revealed Snodgrass had been taken to for medical assessment with suspected concussion.
"He's in hospital at the moment - it's a precautionary one," he said. "He was out, it is concussion and we're hoping that's all it is.
"The medical people were very quickly onto it. They've done the right thing and he's away just as a precaution, but we're hoping he'll be okay."
In a double blow for Norwich, Nathan Redmond also picked up an injury in the match, which saw Chicharito net twice, with Phil Jones and Fabio adding a goal each to send United comfortably into the quarter-finals.
"Nathan just pulled a muscle in his hip," added Hughton. "How bad that will be, we don't know.
"He was sore for that period of time and it wasn't one where he could continue.
"We just need to make sure, because we've picked up a few injuries - we lost Alex Tettey in the last game.
"We've got a tight squad and we've just got to make sure we're not picking up any more injuries."