The Broncos said they were "disappointed" to learn of John Bowlen's arrest and said he was being placed on an indefinite leave of absence from his job as an administrative employee with the team.
"While this is a personal issue, he is accountable to all club and league conduct policies," the Broncos said in a statement on Thursday.
Online records for the Arapahoe County jail showed Bowlen was being held without bail on harassment charges.
According to the Denver Post, he was being held on suspicion of third-degree assault and harassment, both Class 3 misdemeanors.
Pat Bowlen, who is suffering from Alzheimer's disease, announced last July that he was relinquishing day-to-day control of the team and hoped to turn it over to one of his children.
The NFL's domestic violence policy, revamped last August to include more stringent rules in the wake of the Ray Rice case, applies to all team employees.