The league made the announcement Wednesday, about three hours before Game 5 in Boston. The Celtics won 123-101 to take a 3-2 series lead.
In the video, which was posted on Instagram, the Celtics' All-Star can be seen directing a profane remark at a fan at the Verizon Center.
According to the individual who took the video, the fan was heckling Thomas, who was on the bench at the time, throughout the game.
Thomas pointed at the fan and responded with, "I will f--- you up, and you know that."
"Obviously there's a line that you can't cross and, ultimately, get fined for," Boston coach Brad Stevens said. "That's my reaction to it. I think that if he could take it back he would."
The NBA initially said the incident took place in Game 4 on Sunday but later corrected its news release.
Information from ESPN's Chris Forsberg was used in this report.