Green's foul – initially ruled a flagrant-1 during the game – was upgraded to a flagrant-2 after the league's investigation into the incident. Green also received a $25,000 fine.
Green is eligible to play in Tuesday's Game 4. The Thunder lead the best-of-seven series 2-1.
Green kicked Adams as he went up for a shot in the second quarter of the Warriors' 133-105 loss to the Thunder in Game 3 on Sunday.
"After a thorough investigation that included review of all available video angles and interviews with the players involved and the officials working the game, we have determined that Green’s foul was unnecessary and excessive and warranted the upgrade and fine," the NBA's executive vice president of basketball operations Kiki VanDeWeghe said in a statement.
"During a game, players – at times – flail their legs in an attempt to draw a foul, but Green's actions in this case warranted an additional penalty."