Sandusky was released after posting bail, The Forum of Fargo-Moorhead reported.
Lt. Joel Vettel said a police officer saw Sandusky make an illegal turn shortly before 2 a.m. He then allegedly failed a field sobriety test.
Jon Sandusky, 36, has been director of player personnel with the Browns since 2010. He may have been in Fargo on a scouting trip to North Dakota State University, The Forum said.
Jerry Sandusky, 69, a former longtime assistant football coach at Penn State, was sentenced to 30 to 60 years in prison last year for molesting young boys he met through a charity for at-risk youth.