Fargo police Lt. Joel Vettel said an officer spotted Jon Sandusky, 36, making an illegal turn at the intersection of Fourth Avenue and North University Drive about 1:50 a.m.
The officer pulled Sandusky over and determined after administering field sobriety tests that he was driving under the influence.
Sandusky was booked into the Cass County Jail on suspicion of driving under the influence. Jail staff said he posted bail later Tuesday.
Sandusky is also the son of former Penn State assistant coach Jerry Sandusky, who was convicted in June 2012 of 45 counts of child sexual abuse.
The younger Sandusky is in his second season with the Browns after spending nine seasons working for the Philadelphia Eagles.
Matt Russell, director of player personnel, was suspended indefinitely, and Tom Heckert, the director of pro personnel, was suspended for a month.