Ontario County Sheriff Philip Povero said his department's investigation is not criminal and that Stewart was "fully cooperative" and appeared "very upset" over what had happened.
"He was visibly shaken by this accident," Povero said.
A video of the crash at Canandaigua Motorsports Park showed driver Kevin Ward Jr., wearing a black helmet and firesuit on a dimly lit track, walking toward Stewart's car before being hit and hurtled 50 feet.
Povero said the 25-lap race was under caution when Ward was struck. Stewart's car was behind another before he hit Ward.
"The first car swerved to avoid the driver," Povero said.
Povero said the driver was pronounced dead Saturday night at a Canandaigua hospital. Stewart was unhurt.
A witness said it appeared Ward was trying to confront Stewart, the three-time NASCAR Sprint Cup Champion. The video showed Ward standing to the right of Stewart's familiar No. 14 car, which seemed to kick out from the rear and hit him.
"The next thing I could see, I didn't see (the other driver) anymore," witness Michael Messerly said. "It just seemed like he was suddenly gone."
Povero said the 43-year-old Stewart, a frequent competitor at local sprint car events, was questioned and released. The sheriff asked for people who recorded video of the crash to provide copies for investigators to review.
A spokesman for Stewart's racing team called Ward's death a "tragic accident."
"Our thoughts and prayers go out to his family and friends," the spokesman said in a statement. "We're still attempting to sort through all the details."
Stewart's racing team manager Greg Zipadelli said Stewart will race in NASCAR's event Sunday at Watkins Glen, calling the race "business as usual."
The dirt track, about 30 miles southeast of Rochester, canceled the remainder of the race and later posted a message on its Facebook page encouraging fans to "pray for the entire racing community of fans, drivers, and families."
It said a statement on the crash would come later Sunday.
Ward's website said he began racing go-karts in 1998 at age 4, but didn't start driving sprint cars until 2010. The 20-year-old from Port Leyden, New York, was Empire Super Sprint rookie of the year in 2012 and this year was his fifth season racing the Empire Super Sprints.
Stewart was involved in a July 2013 accident at Canandaigua that seriously injured a 19-year-old driver. He later took responsibility for his car making contact with another and triggering the 15-car accident that left Alysha Ruggles with a compression fracture in her back.
After Saturday's accident, ambulances, fire trucks and police arrived within moments, Messerly said. Fans filed out in stunned silence, he said.
The accident Saturday came almost exactly a year after Stewart suffered a compound fracture to his right leg in a sprint car race in Iowa. The injury cost him the second half of the NASCAR season. Stewart only returned to sprint track racing last month. He didn't return to racing in any form until February when preparation forNASCAR's season-opening Daytona 500 began.
Stewart was a spectator at the Knoxville Nationals in Iowa on Tuesday, the one-year anniversary of the accident, and posted on his Twitter account: "Thank you to everyone that worked so hard to get me back to where I'm at today. It's your life, live it!"
Roughly three hours after Saturday night's accident in New York, Donny Schatz, a sprint car driver for Tony Stewart Racing, won the prestigious Knoxville Nationals in Iowa for an eighth time.
"I was just told there was an incident involving Tony. I don't know to what extent or what's happening," Schatz said.
Stewart is co-owner of Stewart-Haas Racing, the four-team NASCAR organization that fields cars for Stewart, Kevin Harvick, Kurt Busch and Danica Patrick. He's struggled a bit this year since returning from his leg injury, and heads into Sunday's race winless on the season and ranked 19th in the standings.
Stewart was scheduled to start 13th on Sunday at Watkins Glen International in south central New York state. He has just five races remaining to either score a win or move inside the top 16 in points to grab a valuable spot inNASCAR's championship race.