Connolly appeared to raise his arm towards a supporter after the ball was thrown at him from the stands as he went to retrieve it.
Brentford chief executive Mark Devlin says the club will assist in any potential Football Association or Football League probe into the incident, which overshadowed the Bees' 1-0 win.
Devlin told Sky Sports News: "We know the spectator involved so we will be talking to him.
"It is very early and there is not a lot else I can say. We will deal with the relevant authorities and we will take part in their investigation."
Connolly, 30, tried to play down the clash by writing on Twitter: "A total blown up incident at the game last night ! Handbags! We move on."