Smith, who was in the second season of a three-year, $12 million deal with the Browns, played in nine games this season, recording one tackle and a pass defensed. He was inactive for Sunday's game against the Pittsburgh Steelers, despite the Browns playing without star defensive lineman Myles Garrett, who was suspended for the remainder of the season.
The roster move comes despite Cleveland's depth issues on the defensive line, and the loss of Smith's girlfriend, Petara Cordero, in September.
Cordero and Smith were pulled over on the side of the highway after Smith's car had a tire malfunction, causing the vehicle to spin and hit the median, according to the team.
After Cordero exited the car without any major injuries, she was struck by an oncoming vehicle. According to a Cleveland police report obtained by the team, she was transported to Fairview Hospital and pronounced dead.
"Words cannot describe the sorrow we feel for Chris following the loss of his girlfriend, Petara," Browns owners Dee and Jimmy Haslam said in a statement in September. "Our entire organization mourns with Chris, his family and the Cordero family. We will do everything possible to offer them our support, comfort and any resources in this most difficult time."
Police said Smith, who was driving the vehicle, wasn't impaired or injured. The other driver that struck Cordero admitted to drinking.
Cordero, 26, and Smith had a daughter together in August. Smith was excused from the Browns' preseason game against the Indianapolis Colts to attend the birth.
Smith, 27, spent the past two seasons in Cleveland, recording two starts in 2018. He has tallied 68 total tackles, 8.5 sacks, three forced fumbles and six pass breakups since entering the NFL in 2014 with the Jacksonville Jaguars.