Brown, who was waived two days after he was replaced by rookie Germaine Pratt in the starting lineup, had started Cincinnati's first eight games before coming off the bench during Sunday's loss to Baltimore.
The Bengals had signed Brown to a three-year, $16.5 million deal in March that included $4.8 million guaranteed and made him the highest-paid linebacker on the team's roster.
The sixth-year player out of Louisville tallied 54 tackles and had a forced fumble and a fumble recovery this season.
On Monday, Bengals coach Zac Taylor said the team needed to see significant improvement from its linebackers.
"Someone needs to step up and be a leader there," Taylor said. "We've been waiting on that and shuffling the lineup around, waiting on someone to step up and be consistent and be a leader in that room. We're still waiting on that."
Brown, who attended Cincinnati's Northwest High, was coming off an abbreviated 2018 season after missing the final seven games with a knee injury. Before that season, he had signed a one-year deal worth $5 million to return to his hometown after spending the first four seasons of his career with the Buffalo Bills.
With Brown's departure, Cincinnati will have roughly $2.5 million in dead money on its books for the next two seasons.