Busch also was penalized 100 championship points, and placed on probation until Dec. 31.
He clipped Tony Stewart on lap 271, sending him into a barrier, then nearly hit a member of Stewart's crew a short time later.
Busch showed his frustration by making contact with Stewart's car on pit road, and was parked for the rest of the race.
"I regret the incident that occurred at Dover and apologize to NASCAR, my sponsors, the fans, my Penske Racing team and Joe Gibbs Racing," Busch said in a statement. "I understand that safety is crucial to the sport and I accept the points penalty, fine and probation that NASCAR has imposed on me."
Celebrity Families of 2014 [PHOTOS]