The FSF claimed Watford had displayed "disrespectful, pernicious and discriminatory behaviour".
Sarr is currently sidelined with a knee injury and has not featured for Watford since November.
"The Senegalese Football Federation wishes to express by this press release its deep condemnation of the disrespectful, pernicious and discriminatory behaviour of the leaders of Watford who seek by all means to prevent a player from playing with his national team," an FSF statement said.
The tournament gets underway next Sunday in Cameroon and runs until February 6, clashing with the European club season.
Having to free Africans is a sore point with some managers and Napoli boss Luciano Spalletti labelled the Cup of Nations an "invisible monster".
Sarr has impressed for struggling Watford this term, scoring five goals in 12 Premier League appearances.
Watford's handling of Sarr's fellow forward Emmanuel Dennis has also been controversial, with Nigeria saying the English club "showed their teeth" when refusing to release him for international duty.
Senegal, runners-up in 2019, are one of the favourites for the African title.
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