The fine is for $25,000, sources with knowledge of the league's ruling told ESPN.com on Monday.
Durant, who attended Drake's show last week in Toronto, was the subject of what the league regarded as a public recruiting pitch from the famed Canadian artist, who was named the Raptors' global ambassador in September 2013.
"Before we leave, I just want to show one of my brothers something," Drake told the crowd. "You know, my brother Kevin Durant was kind enough to come to the show tonight and watch us. I just want him to see what would happen if he came to play in Toronto. Let him know what would happen."
The Oklahoma City Thunder star and reigning NBA MVP then received an ovation from the crowd, which reportedly launched into a "KD" chant.
Durant will become an unrestricted free agent in the summer of 2016, and various teams -- notably his home-state Washington Wizards as well as the New York Knicks, Brooklyn Nets and Los Angeles Lakers -- are positioning themselves to have sufficient salary-cap space to make a run at him.
Drake hosted the 2014 ESPYs.
Information from The Associated Press was used in this report.