Several media reports said Stewart struck Busch Friday night in the presence of NASCAR officials ahead of Saturday's Budweiser Shootout at Daytona International Speedway.
A Charlotte (N.C.) Observer report said Stewart had hit Busch from behind during a practice session, causing Busch's car to slam into a wall.
The Observer reported that as Stewart turned onto pit road, Busch ran him down and twice slammed his No. 2 Dodge into the side of Stewart's No. 20 Toyota.
When Stewart attempted to turn into the entrance of the garage area, Busch cut him off.
Both were summoned to a meeting with NASCAR officials. NASCAR spokesman Jim Hunter said drivers "have to control their emotions in the cars" and added "there could be" fines or other penalties, the Los Angeles Times reported.
"If they want to get out of their cars and do their thing, that's OK with us," Hunter told Fox Sports. "I just hope they're smart enough to keep their helmets on."
The two drivers had a couple of run-ins last season.