Police spokesman Jim Sughrue said Gordon was taken into custody at Wake County Detention Center after being pulled over for going 50 mph in a 35 mph zone on U.S. 70 in northwest Raleigh around 3 a.m. Saturday.
Raleigh police captain Tommy Klein said that to be arrested in Raleigh for DWI, a person has to be "appreciably impaired." Asked if the charge was DWI for alcohol or another substance, Sughrue said, "I can't comment on any tests we gave him or what the results were."
WNCN, the NBC affiliate in Raleigh, reported Gordon's blood-alcohol level was .09, and he admitted to having three drinks with vodka. The legal limit in the state of North Carolina is .08.
When asked if marijuana or other drugs were involved, Sughrue said he couldn't comment. No drug charges were filed.
Gordon was released on a $500 bond. Court records did not list an attorney. Gordon is scheduled for an Aug. 26 court appearance in Raleigh on the charges brought against him.
The individual who paid for Gordon's bond was identified as Haydn "Fats" Thomas, authorities told WNCN. Thomas is a convicted felon who pleaded guilty to gun and drug charges in November. He was sentenced to 36 months after pleading guilty, but the prison sentence was suspended in lieu of probation.
In 2006, Thomas was convicted of a felony for accessing a computer for fraudulent purposes. Thomas also rented the car that former North Carolina basketball player P.J. Hairston drove when he was arrested for misdemeanor marijuana possession in Durham, North Carolina, in June 2013. Charges were dropped, but it was later found that Hairston accepted so many cars paid for by Thomas that he was dismissed from the Tar Heels.
WRAL-TV reported that the car Gordon was driving was registered to Hairston.
Cleveland general manager Ray Farmer found out about the arrest hours after it happened.
"We are aware of the matter and are disappointed to learn of this situation. We will comment further at the appropriate time," Farmer said in a statement.
Gordon's agent Drew Rosenhaus said he had no comment about the arrest.
Gordon, 23, could be facing a one-season NFL suspension for another failed drug test.
According to Pro Football Talk, Gordon's appeal hearing with the NFL has been set for late July, unless the league and NFL Players Association agree on a reduced suspension before then.
He was suspended four games last season, which he attributed to using codeine. On appeal, that was reduced to two games not playing and two games played without pay.
In early June, Gordon pleaded not guilty to a speeding ticket. He was stopped for going 74 mph in a 60 mph zone on May 25. He was fined $187. His passenger was cited for possession of less than 200 grams of marijuana.
He had 87 catches for 1,646 yards last season and became the first player in NFL history to have consecutive 200-yard receiving games.
Gordon also was suspended twice while at Baylor, the second time indefinitely after failing a drug test. He transferred to Utah, where he sat out the 2011 season. After being taken by the Browns in the supplemental draft, he admitted to failing a drug test at Utah as well.
ESPN NFL Insider Adam Schefter, ESPN.com Browns reporter Pat McManamon and The Associated Press contributed to this report.