The 49-year-old has also been banned from involvement with the Springboks on matchdays until next October.
He made the video after July's first-Test defeat by the British and Irish Lions.
World Rugby found the video contained "multiple abusive and insulting comments and attacks on the officials".
And it described his offences as "especially serious and egregious".
Erasmus stepped down from his role as head coach in the wake of the Springboks' Rugby World Cup triumph in 2019 to become South Africa's director of rugby.
