Even without Green and the injured Steph Curry, Golden State still managed a 110-103 victory over the Hawks.
The suspension, which is without pay, cost Green $120,480, ESPN's Bobby Marks reports.
Green apparently called Durant "a b----" repeatedly after he was called out for not passing Durant the ball late in the 121-116 overtime loss to the Los Angeles Clippers, sources told Chris Haynes of Yahoo Sports.
The argument, which also touched on Durant's upcoming free agency, didn't conclude on the court but continued after the team left the floor.
Warriors guard Klay Thompson took the floor in the locker room afterward to underline how important it was for the team to stick together, per Haynes.
General manager Bob Myers said Green took the news of the suspension well and that he was professional about it.
Since Durant joined the Warriors prior to the 2016-17 campaign, Golden State has won back-to-back championships. He's expected to decline his player option after the season to hit free agency once again next summer.