Argentina winger Di Maria was sent off five minutes before half-time of Sunday's 1-0 loss, also Monza's first ever win in the Italian top flight, after lashing out at Armando Izzo.
He later blamed himself for Juve's first league reverse of the season which left them in eighth and seven points behind leaders Napoli.
The 34-year-old will miss the visit of Bologna and Juve's trip to champions AC Milan after the international break, in which he will take part in two pre-World Cup friendlies.
Mourinho ban
Jose Mourinho will miss Roma's visit to his old team Inter Milan following his one-match suspension.
The Portuguese was banned for "entering the pitch in the 11th minute" of his team's 1-0 home loss to Atalanta on Sunday and "ranting at a player from the opposing team".
Roma had feared that Mourinho would be hit with as much as a three-match suspension after his vehement protests at referee Daniele Chiffi for not giving a penalty for a challenge on Nicolo Zaniolo in the second half.
