Marion County Jail spokesman Julio Fernandez said that Johnson is being held without bond on a charge of murder.
Theobald said that Levine was shot in Coke Lot 1 about 2 a.m. An argument preceded the shooting, Theobald told The Indianapolis Star.
The Coke Lot is a popular spot across the street from the speedway, where Indy 500 race fans have set up tents and partied on race weekend for decades.
Levine's mother, Janice Bickel, told The Associated Press that her son went camping in the lot with a group of friends from Kokomo, about 50 miles north of Indianapolis.
Levine had a 3-year-old daughter who lived with him part of the time, Bickel said. He was studying for a business degree at Ivy Tech Community College's campus in Kokomo and also had started training as an apprentice carpenter.
"He was a great guy. He was an excellent father and a wonderful son. He was very focused on where he wanted to go," she said.
Indiana State Police Sgt. Brian Olehy said the race weekend incident is unusual, but it isn't the first shooting. In 2012, a fan was hospitalized after he was shot in the chest after an apparent altercation across from the speedway.
Levine's death was the first violent death on race weekend in Theobald's 16 years with the Speedway Police Department, he told the newspaper, adding that fights were common on race weekend.
"Unfortunately, we still have fights and this fight led to a shooting. The response time was faster than usual, which is why we were able to find witnesses, which led to the arrest," he told the Star.