The Queens Park Rangers midfielder was accused of disrespecting Rachid Taoussi in an exchange of text messages and Moroccan media following his omission from the tournament in South Africa, which starts next week.
"The Moroccan federation and its staff, the federal bureau seeks a written apology from the player," said a statement by the Royal Moroccan Football Federation.
Taoussi dropped Taarabt last month, saying the player had refused to meet him or take any of his calls when the Morocco coach went to see key players on a European tour.
This followed Taarabt being dropped by the coach for his first match in charge in October, when he came into salvage the country's qualifying campaign for the Nations Cup.
Taarabt, described by QPR manager Harry Redknapp as a "bit of a fruitcake" and with a history of infuriating coaches with his antics, walked out on the Morocco side in 2011 when previous coach Eric Gerets benched him for a key Nations Cup qualifier.
He was recalled several months later after a series of profuse apologies.
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