Video replays showed a pole-shaped object hitting Jordan on the head moments after Nabil Fekir had equalised for hosts Betis to draw the last 16 tie level at 1-1 at the Estadio Benito Villamarin.
Sevilla condemned the "violent attack" and said Jordan, 27, was recovering at home after being taken to hospital for assessment.
"Joan left the Benito Villamarin dazed and was taken to hospital, where he was examined and underwent a series of tests required by the protocol due to the concussion," the club said in a statement.
"Sevilla FC condemns the violent act suffered today by Joan Jordan, an unacceptable act in the world of sport committed by an individual who, of course, does not represent the fans of Real Betis or the way of living football in our city."
Alejandro Gomez put Sevilla in front in the 35th minute, but the lead lasted four minutes before Fekir's leveller.
Video replays showed that Jordan was struck from behind and collapsed to the ground holding his head, although reports said he was later able to stand while receiving medical attention.
The Spanish Football Federation (RFEF) announced that the game was suspended, adding: "The RFEF condemns any act of violence on the pitch."
Betis defender Juan Miranda said Jordan exaggerated the extent of his injury.
"We all heard how his coach encouraged him to go down and get dizzy, they knew what they were doing," Miranda wrote on Twitter.