The 27-year-old's decision follows Senegal, who are managed by Pape Thiaw, letting a 2-0 lead slip as they were dramatically beaten by Belgium in their last-32 tie at the World Cup.
Habib Diarra and Ismaila Sarr had deservedly put Senegal in front before late goals from Romelu Lukaku and Youri Tielemans sent the tie into extra time.
Belgium were awarded a controversial penalty in the 125th minute and Tielemans scored from the spot to knock Senegal out.
Gueye, who plays for La Liga side Villarreal in Spain, started the game but was replaced by Lamine Camara after 66 minutes.
"I will come back to say a few words about the elimination... but I am announcing today that as long as this coaching staff is in place, I will be taking a break from the national team," Gueye, who has won 45 caps for Senegal and scored twice in their group-stage win over Iraq, said on social media.
Thiaw has been in charge of Senegal since December 2024 and was at the heart of the controversy which resulted in his side being stripped of the 2025 Africa Cup of Nations title.
Thiaw ushered his team off the field when Morocco who were awarded a stoppage-time penalty in the Afcon final in January.
The players eventually returned after a delay of about 17 minutes before Brahim Diaz's penalty was saved and Gueye scored an extra-time winner.
However, Morocco were declared the winners of the tournament in March when the Confederation of African Football (Caf) overturned the result of the final following Senegal's walk-off.
Senegal have lodged an appeal with the Court of Arbitration for Sport and hope to regain the title.