Clingan hit a superb free kick to put City ahead in the 37th minute of the local derby with Leicester City but injured his foot in a 68th minute tackle and had to be replaced by Isaac Osbourne.
City boss Chris Coleman said to the media afterwards: "Sammy was caught late and was off the pitch when we conceded but what can we do?
"We don't know how bad the injury is yet - we need to see it when the swelling goes down, but it's quite badly bruised."