O'Neal missed the Cavs' game Friday night at Toronto and is scheduled to have an MRI on Saturday.
"I don't know how long Shaq will be out," Brown said after Cleveland's 108-88 victory over Boston.
Brown could not say how O'Neal was hurt, but it appeared to be when Glen Davis blocked his shot with just over 7 minutes left in the first half. The Cavaliers called a timeout soon after to take O'Neal out of the game, and they later issued an injury report saying he had a "significant right thumb sprain" and would not return.
O'Neal was not available for comment.
"We need him out there," Cavaliers forward LeBron James said. "We play faster without Shaq in the lineup ... but in the playoffs you can't play fast all the time. You need to establish the half-court offense. That's what he does for us."
His absence is even tougher to overcome because the Cavaliers traded backup center Zydrunas Ilgauskas to Washington before the trade deadline.
The Wizards bought out Ilgauskas' contract Thursday and was waived. Under NBA rules, he must wait 30 days before he can re-sign with the Cavaliers. However, he is allowed to sign with another team immediately, and several have expressed interest in him.
O'Neal had six points and two rebounds before leaving.
Information from The Associated Press was used in this report.