The federation said Watford had told them on Friday they would not be releasing the highly rated forward for the tournament in Cameroon, which kicks off on Jan. 9 and where Senegal are one of the favourites.
The Premier League club responded with a statement in which they said Sarr has not been fully fit since suffering a knee ligament injury during a 4-1 win over Manchester United on Nov. 20 and have informed Senegal of the winger's timeframe of recovery.
"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," said a statement signed by the Senegal Football Federation [FSF] 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," it continued.
It added Senegal would take the matter up with FIFA if "Watford persists in its deliberate refusal to release the player".
"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.
"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," it added.
In response, Watford said: "Ismaila Sarr suffered a knee ligament injury on Nov. 20 in the match against Manchester United and has not been fit to play for Watford since that date.
"In early December, the club wrote to the Senegal Football Federation outlining the clinical diagnosis of Ismaila's injury and immediately followed that up by supplying the MRI scans detailing the extent of the injury. After further consultation with medical experts, we informed the Federation of Ismaïla's rehabilitation process and likely timeframe of recovery.
"Within the past 10 days, the club has reiterated to the Senegal Football Federation the player's current medical status and recovery schedule.
"The Hornets have have also invited the Senegal Football Federation to instruct their own independent surgeon to confirm the diagnosis and rehabilitation period."
The Premier League strugglers have already refused to allow Nigeria striker Emmanuel Dennis to join up with his country, saying the Nigerian Football Federation did not call him up in time, missing the deadline to inform the club of his selection.
Nigeria did not contest the claim and have since replaced Dennis in their squad.
Watford, who lost in stoppage time to Tottenham Hotspur on Sunday and slipped closer to the relegation zone, will lose three other players to the tournament -- William Troost Ekong of Nigeria and the Moroccan pair of Imran Louza and Adam Masina