The 32-year-old basketball player had made misogynistic and homophobic comments in private Instagram messages to actor Michael Rapaport after he criticized him after an interview in connection with a match in December.
"I receive threats and disgusting messages daily, but never in my wildest imagination did I think @ KDTrey5 (Durant) would be one of them," Rapaport wrote in a tweet containing several screenshots from the conversation.
"The snake itself threatens me, picks up my wife and wants to fight," he writes.
The NBA says in a statement that Durant is fined for using "an offensive and derogatory language on social media".
Durant has issued an apology after the incident and says he did not know that his actions were inappropriate.
- I'm sorry that people have seen the language I used.
That's not how I want people to see or hear from me.
But hopefully I can move on and get back on track, he says according to AFP.
CLIP: Here the basketball star puts 102 threes - in a row (27 Dec 2020)
Javascript is disabled
Javascript must be turned on to play video
Read more about browser support
The browser is not supported
SVT does not support playback in your browser.
We therefore recommend that you switch to another browser.
Read more about browser support
Stephen Curry offered a show at the training.
Photo: Bildbyrån.