The 23-year-old was stopped in the early hours of July 5 by police in Raleigh, North Carolina and was charged and incarcerated for the DWI. However, he has since been bonded out of jail.
The Browns have revealed that they are disappointed with the receiver for the incident, but refused to provide any further comment on the issue.
"We are aware of the matter and are disappointed to learn of the situation," Browns general Ray Farmer said in a statement. "We will comment further at the appropriate time."
Gordon is already facing a year-long suspension from the NFL after failing a drugs test earlier in the off-season.