General Manager Danny Ainge sat next to Durant's mother during the Big 12 tournament. The league said Ainge violated rules demanding that contact be kept to a minimum between team executives and potential NBA draft picks, until college players officially declare for the draft.
Sports Illustrated first reported the story on its Web site.
Celtics spokesman Jeff Twiss said Ainge is on the road scouting players and he did not offer specifics of the fine.
The Celtics won in San Antonio for the first time in 17 years on Saturday, topping the Spurs 91-85. At 20-46 on the year, the team has the league's second-worst record behind the Memphis Grizzlies.