Gordon was charged with DUI and also received a speeding citation for driving 50 mph in a 35 mph zone, WKYC reported.
He was booked at 4 a.m. into the Wake County Detention Center.
"We are aware of the matter and are disappointed to learn of this situation," Browns general manager Ray Farmer said in a statement. "We will comment further at the appropriate time."
Gordon is, meanwhile, awaiting word on his appeal with the NFL, which may ban him from the league for one year for violating its drug policy.