Glover was hit by a metal bucket as fans from the Victory end stormed onto the pitch after the 20-minute mark of the game with City up 1-0 at Melbourne Rectangular Stadium.
The goalkeeper was escorted off the pitch with blood streaming down the side of his face and referee Alex King found himself surrounded by fans, who had threatened to protest a move to shift the next three A-Leagues Grand Finals to Sydney.
Football Australia said in a statement: "Such behaviour has no place in Australian Football, with a full Football Australia investigation to commence immediately, where strong sanctions will be handed down."
Glover was reportedly targeted after throwing a flare that landed on the pitch back into the crowd. His team later said he suffered a suspected concussion in the incident.
A flare also appeared to hit a Network 10 cameraman covering the match.
Players and officials left the pitch and the match was abandoned as police were called to control the crowd.
"The Australian Professional League is coordinating with Football Australia regarding the ramifications of these events," the APL said in a statement.
Victory said in a statement that they were devastated and they condemned the behaviour of their fans.
"The actions that occurred... are not acceptable under any circumstance and have no place in football," Victory said. "The security and welfare of everyone involved in a football match is paramount and the club will not accept this behaviour.
"The club would like to formally apologise to Glover, King and the camera operator as well as all players, officials and those who witnessed the appalling behaviour."
The club added they would work with stadium officials and the Victoria Police for a full investigation.
Australia's top-flight soccer competitions have sold their title-deciding Grand Finals to Sydney until 2025 in a deal condemned by fans.
Both sets of Melbourne fans had originally planned to leave the game at the 20-minute mark to protest the move.
The A-League Men and Women's competitions have traditionally played their championship deciders at the highest-placed teams' home grounds.
