Play was halted and both sides left the field with the game abandoned.
"Tom Glover is receiving medical treatment in the dressing room and likely has a concussion," City tweeted, with pictures showing a gash on his face.
A match official was also injured, Football Australia said.
"Following shocking scenes ... where fans from the Melbourne Victory FC end entered the field of play, Football Australia match officials have abandoned the match," it said.
"Such behaviour has no place in Australian football, with a full Football Australia investigation is to commence immediately, where strong sanctions will be handed down."
