The incidents happened outside the club's Trigoria sports complex on Tuesday evening after a training session.
One supporter allegedly stopped the car Barusso was travelling in before punching a window and kicking the vehicle.
That reaction was said to be provoked by Barusso's insistence to remain at Roma after refusing a number of offers to leave the club.
Okaka was attacked after allegedly refusing to sign some autographs, but the club have thrown their weight behind the players via an official statement.
"A.S Roma S.p.A are saddened by the incidents against Ahmed Barusso and Stefano Okaka outside Trigoria on Tuesday.
"We want to remind everyone that the club are fully behind their players and hope the relationship with the fans can continue to be respectful regardless of decisions from the players in relation to the transfer market."
Barusso joined Roma in 2007 and made his debut under former coach Luciano Spalletti.
However, since then he has spent a number of years on loan at various clubs, most recently with Livorno.
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