The NBA announced the fine Tuesday against Green for the incident involving Minnesota Timberwolves center Gorgui Dieng. The league, though, spared the Houston Rockets guard from suspension.
Green was seen shoving Dieng after the Dieng sent Paul to the floor in the fourth quarter.
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Green had to be separated from Dieng, and he was ejected from the game.
Paul told reporters after the game that he'll foot the bill for any fine his teammate will draw.
Green sounded contrite over his actions.
"I learned my lesson, got ejected, try not to get that again and hopefully we're going to move forward from this," Green said.
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Green, a Houston native, was signed by the Rockets in December 2017 as injury relief for James Harden at the time. He was then signed through the rest of the year on a veteran minimum salary of $1.3 million.
Paul approved a player option of $24 million with the Clippers before being traded to Houston.
Green scored 12 points off the bench in 15 minutes before heading to the locker room early in Sunday night's win.
Green is expected in the lineup when the Rockets visit the Trail Blazers in Portland on Tuesday night.