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The son of Denver Broncos owner Pat Bowlen was arrested for domestic violence in Colorado on Wednesday ... while wearing a Broncos shirt ... TMZ Sports has learned.

29-year-old John Bowlen Jr. -- one of 7 Bowlen children -- is being held at the Arapahoe County jail outside of Denver on suspicion of 3rd degree assault and harassment.

According to the police report, the victim told police John was under the influence of whippets and alcohol. Whippets is slang for nitrous oxide.

The woman -- who says she has been dating Bowlen for 10 months -- says the two were inside of John's apartment when John began acting strange and "shoved her against the wall."

The woman says she called 911, but John took the phone and hung up.

When the operator called back, John reportedly answered and said, "This is the owner of the Denver Broncos. I am sorry. K. Nothing is wrong. This is John Bowlen."

The woman says she had been drinking alcohol earlier in the evening.

John was taken into custody for domestic violence harassment and property crimes. He's being held without bail.

According to multiple reports, John has an MBA in sports and entertainment from the University of Denver and is in executive training with the Broncos. He is one of the frontrunners to take over the team when his father (who is suffering from Alzheimer's) steps down.

Pat Bowlen isn't the only Broncos executive with a son who's been accused of domestic violence -- last year the son of Broncos General Manager John Elway, John Elway III, was arrested and convicted of attacking his GF during a heated argument in Arizona.

The Denver Broncos have released a statement saying, "We are disappointed to learn of the matter involving John Bowlen ... . While this is a personal issue, he is accountable to all club and league conduct policies. As such, John will be placed on an indefinite leave of absence from the organization."