Sarr has been named in the Senegal squad for the tournament, which runs from January 9 to February 6, although he has not played for the Hornets since November 20 against Manchester United when he suffered a knee injury.
Watford insist the player is injured but Senegal want him to report for preparations nonetheless.
"The English club Watford notified on the basis of spurious arguments its decision to block the player Ismaila Sarr, who has expressed his desire to join the Senegalese selection for the Cup of Nations," read a statement signed by the Senegal Football Federation general secretary Victor Seh Cisse.
"The FSF responded immediately to confirm the player's call-up and the club's obligation to release the player by no later than Jan. 3.”
"The FSF wishes to express its deep condemnation of the disrespectful, pernicious and discriminatory behaviour of Watford who seek by all means to prevent a player from playing with his national team,” it continued.
"Africa, its football and its footballers deserve the same respect as that accorded to other continents, confederations and players.
"The FSF will take all the necessary action to ensure that the basic right of its footballers to play for their country is respected.”
Watford are also in a row with Nigeria over their refusal to release Emmanuel Dennis for the tournament.