The most widely followed motorsports organization in the United States said the new rule would require drivers involved in accidents to remain in their car unless it was unsafe to do so due to fire or smoke.
A track safety official would then direct the driver to leave the car and walk directly to an ambulance or other vehicle.
The new rule puts into the books something that had "been informal, just an understanding," said Robin Pemberton, NASCAR's vice president of competition and racing development.
Stewart struck Kevin Ward, Jr., 20, during a dirt track race last Saturday in upstate New York after Ward left his car and pointed at Stewart while standing in the middle of the track.
"You have to recognize when you get a reminder or tap on the shoulder, something that may need to be addressed," Pemberton told a news conference at the Michigan International Speedway in Brooklyn, Michigan.
"It was time to address this."
No charges have been filed against the 43-year-old Stewart, one of the sport's biggest names. The investigation has not yet been completed.
Stewart will not take part in the Michigan 400 on Sunday, the second straight NASCAR race he will skip following the deadly incident in Canandaigua, New York, his team said.
Jeff Burton will take Stewart's place in the race. Brett Frood, the executive vice president of Stewart's race team, Stewart Haas Racing, said the decision to bow out "was Tony's."
"An emotional week for him. He's grieving," Frood told reporters. "He made the decision he's not ready to get in the race car and will take it week by week. It will be up to Tony when he's ready to get back in the car."
Stewart and Ward bumped cars during last Saturday's dirt-track race, and the impact sent Ward's car careening into an outside retaining wall.
As the caution flag came out, Ward jumped angrily out of his car and walked to the middle of the track as Stewart, who remained in the race, came around on the next lap.
Investigators are trying to determine if Stewart hit the throttle as he approached Ward because his car appeared to fishtail before striking Ward.
Authorities have said they do not have any evidence of wrongdoing by Stewart. Frood said Stewart's sponsors, which provide millions of dollars to the race team, were unwavering in their support.
Skipping Sunday's race eliminates Stewart from the Chase, NASCAR's version of the playoffs.
"I'll be honest, the Chase is of the lowest priority as it relates to Tony right now," Frood said. "Right now it's about getting Tony in a better place than he is. When he's ready to do that, he'll get back in the car."
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