Griezmann was booked for diving during the second half as Atletico sought to haul back a 2-0 deficit and referee Juan Martinez Munera dismissed him almost immediately for his reaction to the punishment.
The report handed in by the official said Griezmann had called him "cagon", which translates as "chickens***".
The Royal Spanish Football Federation's (RFEF) disciplinary committee deemed the France star's reaction to be "unjustifiable" and an act of "contempt and disregard" towards Munera.
Griezmann will miss Atletico's matches against Las Palmas and Valencia and must also pay a €600 fine, with his club culpable for €700.
Meanwhile, Real Madrid captain Sergio Ramos has received a one-match ban as expected after collecting two bookings during the champions' 3-0 win at Deportivo La Coruna.
Zinedine Zidane's men host Valencia on Sunday.