Race officials said 14 fans were sent to nearby hospitals and another 14 were treated at the Florida track, which will host the prestigious Daytona 500 race on Sunday.
"Stuff was flying everywhere," spectator Terry Huckaby, whose brother was sent to the hospital with a leg injury, told the ESPN sports network. "Tyres were flying by and smoke and everything else."
Among the injured were a 14-year-old boy in critical but stable condition, and a man who was in surgery for a life-threatening head injury, according to ESPN.
Joie Chitwood, president of the Daytona International Speedway, said Sunday's main race would go ahead despite the incident as crews were repairing the track and the grandstand.
"First and foremost, our thoughts and prayers are with our race fans," Chitwood said. "Following the incident, we responded appropriately according to our safety protocols and had emergency medical personnel at the incident immediately."
Tony Stewart won the race at Saturday's event, which is the curtain-raiser for American stock car racing's biggest event on Sunday which will feature Danica Patrick as the first woman to start on pole position.
Saturday's wreck happened after driver Regan Smith, who was leading the race, attempted to block another driver as they were nearing the checkered flag and hit the other car, a report on the NASCAR website said.
"My fault," Smith, who finished 14th, told the site. "I threw a block. I'll take the blame for it. But when you see the chequered flag at Daytona, you're going to block, and you're going to do everything you can to be the first car back to the stripe. It just didn't work out today. Just hoping everything is okay, everyone who was in the wreck and all the fans."
The crash sent driver Kyle Larson's car airborne and ripped out its engine, although he climbed out of the wreckage afterward unhurt.
"I was getting pushed from behind, it felt like," Larson told ESPN after the crash.
"By the time my spotter said, 'Lift,' or to go low, I believe, it was too late and I was in the wreck. Then I felt like it was slowing down, and it looked like I could see the ground, and had some flames in the cockpit. Luckily, I was all right and could get out of the car quick," he added.
The injured were carried away on stretchers from the chaotic scene in the stands. They were taken to Halifax Health Medical Center and Florida Hospital Memorial Medical Center in Daytona Beach.
NASCAR's vice president of race operations, Steve O'Donnell, said that the fencing, which was ripped through by the flying debris, was being replaced and the incident would be reviewed.
"We're very confident that we'll be ready for tomorrow's event with the 55th running of the Daytona, but as with any of these incidents, we'll conduct a thorough review, we'll work closely with the tracks as we do for all our events, learn what we can and see what we can apply in the future," he said.
It is rare that spectators get hurt in American racing, but it has happened before. In 2009, Carl Edwards's car slammed into the catch fencing at Talladega and injured nine fans. Three were killed in Charlotte, North Carolina, a decade earlier in the IndyCar Series, and three others were killed in 1998 in Michigan during CART's US 500.