Authorities in New York state said that they had found no evidence of criminal behavior and that Stewart, a tempestuous racer and one of the highest-paid drivers in NASCAR, was cooperating with investigations into Saturday night's death.
Earlier in the day, the 43-year-old Stewart withdrew from Sunday's high-profile NASCAR Sprint Cup Series at Watkins Glen, New York, but only after a storm of criticism on social media when a team official told reporters that Stewart was proceeding with "business as usual."
Ontario County Sheriff Philip Povero said no evidence of criminal intent had been found in the death of driver Kevin Ward Jr., 20.
"At this very moment, there are no facts in hand that would substantiate or support a criminal charge, or indicate criminal intent on the part of any individual," Povero told a news conference.
In the low-stakes race at Canandaigua Motorsports Park, about 25 miles (40 km) southeast of Rochester, Stewart appeared to have clipped Ward's car and caused it to spin out of the race, according to videos posted online.
Ward, of Port Leyden, New York, stepped out of his car and onto the track as he seemed to gesture at Stewart, a three-time NASCAR champion, before he was struck and killed, according to the videos.
The crash occurred on a dimly lit section of track and the race was under a yellow flag, or caution, Povero said.
Ward was pronounced dead at a hospital. WSYR-TV in Syracuse reported that Ward's family was at the track at the time of the crash.
"There aren't words to describe the sadness I feel about the accident that took the life of Kevin Ward Jr.," Stewart said in a statement.
Stewart, of Columbus, Indiana, is NASCAR's fourth-highest paid driver, with an estimated $17.3 million in earnings this year, according to Forbes.
His sponsors include Bass Pro Shops, Mobil 1, Coca-Cola and Chevrolet. Stewart co-owns Stewart-Hass Racing, a four-car outfit whose drivers include female standout Danica Patrick.
A.J. Allmendinger, the winner of Sunday's NASCAR event, offered condolences to the Ward family.
"We are racing with heavy hearts today," he said on the ESPN television network.
Ricky Craven, an ESPN analyst and former NASCAR Cup driver, said on ESPN he thought a rule was needed that a driver would be penalized if he or she left a car before a security crew arrived.
He added that there was a 50-50 chance that Stewart would compete next week at NASCAR's Pure Michigan 400.
NASCAR, which was not involved in the Saturday race, endorsed Stewart's withdrawal from the Watkins Glen race. It said in a statement that it was monitoring the situation.
The National Association for Stock Car Auto Racing is the sanctioning body for one the most popular sports in the United States. It oversees more than 1,200 races that are broadcast in more than 150 countries and in 20 languages.
More Fortune 500 companies participate in NASCAR than any other sport, according to the racing body.
Stewart began his career on dirt tracks and enjoys going back to his roots, despite the modest pay compared with the NASCAR circuit.
Stewart has occasionally gotten into fights with other drivers, including a shoving match with Joey Logano at the Auto Club 400 NASCAR Sprint Cup race in Fontana, California, last year.
Among his most celebrated accomplishments was racing in 2001 in the Indianapolis 500 and the Coca-Cola 600 in Charlotte, North Carolina, on the same day. He is the only driver to complete all 1,100 miles (1,800 km) in what is known in racing circles as Double Duty.
Stewart was involved in an accident at Canandaigua in July 2013 that injured another driver.