Gilbert received a citation for failure to control his vehicle, and he was not injured in the crash, Sgt. Daren Lubinsky said. His car had to be towed because of damage to the undercarriage.
A Browns spokesman said Gilbert made the team aware of the incident. The spokesman did not have further comment.
The Browns will open the regular season Sunday on the road against the New York Jets. It's unclear whether Gilbert will still travel with the team to New Jersey on Saturday.
Lubinsky said the incident began when Gilbert and a Parma man whose name the police are not disclosing were involved in a traffic altercation while traveling southbound on Interstate 71 South in Middleburg Heights.