The incidents occurred after Green made 3-pointers with 5:33 and 5:12 left in Miami's 110-105 victory over Washington on Wednesday night.
Green appeared to make gun and throat-slash gestures after each shot.
Green, who finished with 28 points, joined the Heat as a free agent in July, when he signed a one-year deal worth $1.4 million.
The Associated Press contributed to this report.
Gerald Green fined $25K for menacing gestures
Heat guard Gerald Green is fined by the NBA for his celebration during Miami's preseason win over Washington.