"We believe Clinton has dislocated his shoulder," Blues boss Steve Bruce said immediately after the game.
"He's in hospital as we speak and we'll be going to see how he is.
"The doctors are with him at the moment and I'll not know until later on this afternoon the full extent of the injury."
Morrison must now be doubtful for the Republic of Irelands Euro 2004 qualifier against Georgia in Tbilisi next Saturday.
West Brom Match Report