Greg Zipadelli, the competition director for Stewart-Haas racing, announced the decision Sunday morning. Regan Smith raced in place of Stewart.
Stewart released a statement Sunday afternoon.
"There aren't words to describe the sadness I feel about the accident that took the life of Kevin Ward Jr. It's a very emotional time for all involved, and it is the reason I've decided not to participate in today's race at Watkins Glen. My thoughts and prayers are with his family, friends and everyone affected by this tragedy," he said.
Sheriff Philip Povero said Sunday afternoon that there are no charges pending at this time. The District Attorney is continuing to investigate the accident but there is no evidence to support criminal charges or intent at this time, he said.
Ward's family also released a statement Sunday afternoon.
"We appreciate the prayers and support we are receiving from the community, but we need time to grieve and wrap our heads around all of this."
Earlier Sunday, Zipadelli said Stewart, a three-time NASCAR champion, felt strongly he shouldn't race at Watkins Glen following Ward's fatal accident. He said it was Stewart's decision not to race.
"I support Tony Stewart. I think I have shown that over the last 18 years," Zipadelli said.
Before the announcement that Stewart wouldn't race, Zipadelli had said Stewart would drive in Sunday's race, calling it "business as usual." The race is critical for Stewart's championship chances but he decided to sit out the race after taking "some time to sleep on it," Zipadelli said.
"[Stewart] feels strongly this is the right thing to do. We at SHR support it and agree with it. It's a difficult time for both parties. This is what we feel is right and we're supporting Tony in it," Zipadelli said.
"Our thoughts and prayers go out to the family, friends, and fellow competitors of Kevin Ward Jr.," NASCAR said in a statement Sunday. "We support Tony Stewart's decision to miss today's race and we will continue to respect the process and timeline of the local authorities and will continue to monitor this situation moving forward."
Bass Pro Shops, which is Stewart's primary sponsor, said in a statement that it was "deeply saddened" by the accident.
"We send our thoughts and prayers to the family and friends of sprint car competitor Kevin Ward Jr. and also to Tony Stewart and everyone at Stewart-Haas Racing," it said in the statement.
Stewart was unhurt in Saturday night's accident.
A video of the crash at Canandaigua Motorsports Park showed driver Ward, 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 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.
Ward, 20, was pronounced dead Saturday night at a hospital in Canandaigua.
The sheriff is asking for people who have video of the crash to contact the office so copies can be obtained for review.
"People that witnessed it were horrified," Povero said of the crash. "They were extremely shocked."
Video of the crash showed Ward, in the No. 13 car, spin into a wall after contact with Stewart's car. The video showed Ward climb quickly from his car and briskly walk around it in what appeared to be an attempt to confront Stewart as he passed by in his own car, Stewart's familiar No. 14.
The video showed Ward to the right of Stewart's car, which seemed to kick out from the rear and hit Ward. The driver was hurtled through the air and emergency personnel quickly reached Ward as he lay on the track.
Dale Earnhardt Jr. and Jimmie Johnson were among drivers to tweet their condolences to Ward's family on Sunday.
We will all loose someone in our time. When a loss is sudden and unexpected, the pain & sadness is suffocating. Prayers for the Ward family.
- Dale Earnhardt Jr. (@DaleJr) August 10, 2014Racing with a heavy heart today... Thoughts and prayers for the Ward family.
- Jimmie Johnson (@JimmieJohnson) August 10, 2014The accident came just four days after the one-year anniversary of an accident in a sprint car race in Iowa in which Stewart suffered a compound fracture to his right leg. The injury cost him the second half of the NASCAR season.
The track, about 30 miles southeast of Rochester, canceled the remainder of Saturday's race within five minutes and later posted a message on its Facebook page encouraging fans to "pray for the entire racing community of fans, drivers, and families."
Stewart was involved in a July 2013 accident at Canandaigua Motorsports Park 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.
Stewart only returned to sprint track racing last month, almost a year after breaking his leg in the crash in Iowa. He didn't return to racing in any form until February, when preparation for NASCAR's season-opening Daytona 500 began.
He refused to stop his extracurricular racing despite the injury. The multimillionaire is known to participate in races with purses worth less than $3,000 and drive alongside drivers of varying ages and talent levels.
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!"
Even though he did not race Sunday, Stewart can still make the Chase if he wins before the Chase. Including Sunday, there are five races before the Chase (Watkins Glen, Michigan, Bristol, Atlanta, Richmond).
The new Chase rules state that a driver must attempt to qualify for all 26 races before the Chase (unless they are given an injury exemption). Stewart qualified his car, but since he won't start the race, he won't receive any points.
ESPN.com's Brant James and Darren Rovell, ESPN Stats & Information and The Associated Press contributed to this report.
No Criminal Charges Pending Against Stewart
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Marty Smith discusses Tony Stewart's decision to not race at Watkins Glen on Sunday after he struck and killed sprint car driver Kevin Ward Jr. in a race on Saturday night.
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Ricky Craven discusses the decision by Stewart-Haas Racing to not let Tony Stewart drive in Sunday's NASCAR Sprint Cup race after he struck and killed sprint car driver Kevin Ward Jr. on Saturday night.