A viral video on social media showed a man kicking the ball from a nearby rooftop towards the stadium, where it appeared to bounce off the roof, while a separate clip showed staff carrying it away.
"Brentford Football Club is aware of an incident involving an item being kicked from a height towards the field of play during Saturday's match against Liverpool," the club said in a statement.
"Such behaviour is dangerous and potentially very harmful.
"The matter has been referred to the police and the club is supporting the relevant authorities in their investigation to help identify those responsible and take appropriate action, which may result in criminal prosecution.
"The matchday safety of fans, staff, players and officials is of utmost importance, and the club will support all efforts to ensure action is taken."
Brentford lost the game 2-1 after surrendering a first-half lead and finishing with nine men.
The Gtech Community Stadium is surrounded by residential and commercial buildings.
Brentford are sixth in the league standings with 10 points from seven matches and visit Hull City on Sunday.