The incident came following the Nextel Cup Dodge/Save Mart 350.
Stewart lost 25 points in the driver standings, falling from fifth to sixth place, and is on probation through Aug. 18. Car owner Joe Gibbs also lost 25 points in the owner standings.
"This action we've taken speaks for itself," NASCAR president Mike Helton said. "Tony Stewart is well aware of what is expected of him going forward."
Stewart ran into the rear of Vickers' car during the race, then sought him out in the garage area. When Vickers apparently laughed off Stewart's criticism, Stewart shoved his hand into Vickers' chest and grabbed him by his uniform before being pulled away by crew members.
Notable deaths of 2014 [PHOTOS]