Bryant was in possession of Adderall at the time of his arrest, Ohio Highway Patrol spokesman Craig Cvetan told NFL Media. Police also found marijuana in the car, along with a concealed handgun lacking a permit and a second firearm.
Bryant remains on the roster, but the Browns benched him for the final two games of the year and he's now a candidate to be suspended by the NFL.
Bryant was previously arrested on a DUI charge in Oklahoma in May 2013. He pleaded no contest. In college, Bryant also reportedly pleaded no contest for allegedly selling marijuana in a parking lot at East Central University.
It's a blow for Cleveland's defense after the hybrid end/outside linebacker recorded a career- and team-high 5.5 sacks in 2015. With 31 appearances over three seasons, Bryant -- due $675,000 next season -- has showed flashes of disruption and power off the edge.
His future is now in doubt for a club starting over once again under new coach Hue Jackson.