Childress, 65, punched Busch, 26, several times during an altercation in the garage area shortly after the 250-mile Camping World Truck Series race Saturday at Kansas Speedway.
The incident now means Childress is on probation for all NASCAR-sanctioned events for the rest of the year.
"We feel this action is appropriate and are confident all parties involved understand our position on this matter and will move forward appropriately," the racing organization said in a release.
Childress said in a statement he accepts NASCAR's penalty.
"First of all, I'm responsible for my actions, plain and simple," he said. "As you know, I am a very principled person and have a passion for what we do at Richard Childress Racing. I believe passionately in defending my race teams and my sponsor partners. In this instance, I let that passion and my emotions get the best of me."
Busch and Childress' driver, Joey Coulter, had hotly contested the final laps of the truck race. Coulter passed Busch on the last lap to finish fifth, while Busch ended sixth.
Once the race was over, Busch hit the side of Coulter's truck on the cool- down lap, setting the stage for the Childress-Busch confrontation.
Busch is on probation until June 15 for all NASCAR events due to an altercation he had with Kevin Harvick in a May 7 Sprint Cup race at Darlington Raceway.
Saturday's incident was not a violation of his probation, NASCAR ruled.
Jordana Brewster on Paul Walker: 'He was an enormous presence in my life'
Couple mistakenly served bag of cash at McDonald's drive-thru