Favre, 58, went off the road at 5:23 p.m. near Kiln, the home town of Brett Favre, and ran into a ditch, Sgt. Joe Gazzo with the Mississippi State Highway Patrol told the Associated Press.
"It didn't appear that the accident was serious enough to cause him to be unconscious, so that leads us to believe that a medical condition was what caused him to go off the road," Gazzo said.
Irvin Favre was pronounced dead at 6:15 p.m., Gazzo said.
An autopsy will be performed Monday but the preliminary reports indicated that he died of a heart attack or stroke, Gazzo said.
"First, the witnesses, then the ambulance, and then at the hospital they tried to revive him," Gazzo said.
"It's going to be a great loss to the community, he was a great guy," said Gazzo, who, like many in this tight-knit area of southern Mississippi, said he knew the Favres.
ESPN reported tonight that Brett Favre is "questionable" for Green Bay's Monday night game against the Raiders in Oakland. A decision will be made Monday morning on if he will play against the Raiders.
Last year in early December, Bola Gbaja-Biamila, the mother of Kabeer Gbaja-Biamila, died in an automobile accident near her home in Los Angeles. The accident occurred less than 24 hours after Kabeer Gbaja-Biamila's wife, Eileen, gave birth to their first child and after the Packers beat the Chicago Bears in a game at Lambeau Field. Despite traveling back and forth to Los Angeles and missing some practices, Gbaja-Biamila played in the Packers' next game against the Minnesota Vikings.
Also last December, ex-Packers defensive end Vonnie Holliday was informed the night before a game against the Buffalo Bills that his cousin had died in an accident. Holliday went on to play in the game and recorded a season-high five sacks.
The remarkable Brett Favre has started an NFL quarterbacks record of 204 straight games, including the playoffs, but he often has said that the streak does not mean anything to him.
Bus Cook, Brett Favre's agent, said the elder Favre apparently had a massive heart attack while driving.
"Right now funeral arrangements are incomplete," he told the Associated Press. "Of course, I don't know what Brett's going to do. ...
"I know his dad would insist that he play the game," said Cook, who had known the senior Favre for about 15 years, ever since Brett Favre graduated from college. "No question. His dad would tell him get out there and play."
Irvin Favre was his son's football coach at Hancock North Central High School in Mississippi.
"Be hard to focus and concentrate maybe, but if anybody can do it he can," Cook added.
In California, Packer right guard Marco Rivera said news of the death was spreading among team members.
"Just put it this way, we're all in shock," he said. "Right now we're finding out about it one by one. I just saw it on the news."
The Packers had not yet held their team meeting Sunday night.