The citation from Berea Municipal Court in Cuyahoga County says that Browns teammates De'Ante Saunders and Bryant were stopped in a 2015 green Dodge traveling 75 mph in a 60 mph zone. Saunders, who was driving, refused a breathalyzer test.
The State Highway Patrol said Saunders was cited for driving under the influence. Patrol spokesman Lt. Craig Cvetan also said a gun was confiscated from Saunders' car.
Browns GM Ray Farmer sent out a statement Saturday morning saying the team was aware of the fact that Bryant, who is second on the team with 5.5 sacks, and Saunders, a member of the team's practice squad, were arrested after a traffic stop.
"These are charges that we take very seriously," Farmer said. "The importance of responsible decision-making is something we continually stress to all members of our organization, which makes it extremely disappointing that these two individuals would put themselves in this situation by making such poor decisions."
Information about the gun will be forwarded to the Cuyahoga County Prosecutor's Office because Saunders does not have a concealed weapons permit, Cvetan said.
Farmer added that the incident is subject to the NFL's personal conduct policy.
WOIO TV in Cleveland first reported the arrests.
This is not Bryant's first run-in with the law. He was arrested for selling marijuana when he was at East Central University in Oklahoma in 2012. After being drafted by the Browns in 2013, he was arrested for driving under the influence near the school's stadium.
Information from The Associated Press contributed to this report.