Wayne Bengston, 41, then beat his wife, took his two-year-old son to a relative's house and drove to his home about 40 kilometres away, where he apparently killed himself, police say.
Bengston's wife told police that Rodriguez was in town on business and visiting her at her mother's house when her husband showed up on Thursday night.
It wasn't clear how Rodriguez and the woman were acquainted.
After the shooting, sheriff's deputies found Bengston's truck parked in his driveway.
Efforts by a police SWAT team to contact Bengston inside the house were unsuccessful, and officers found the man's body with an apparently self-inflicted gunshot wound to the head, police said.
Besides appearing on TV, Rodrigues was the founder and CEO of Global Adventure Outfitters. According to the outfitters' website, he was an editor at Shooting Times Magazine and a contributing editor at Petersen's Hunting, Guns & Ammo and Dangerous Game.
He was a mortgage banker before founding Global Adventure Outfitters, and he has hunted in 21 countries, the website says.
"A Rifleman's Journal" tracks Rodriguez's hunting travels to exotic locations, according to a Sportsman Channel description.
He has a wife and two children, it says.
A woman who answered the phone at Global Adventure Outfitters on Friday confirmed Rodriguez had been in Montana.
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