Senegal squandered a two-goal lead against Belgium before losing 3-2 in extra time in the round of 32.
"I will come back to tell you a few words regarding the elimination … but I announce today that, as long as this technical staff remains in place, I'll be taking a break from the national team," the 27-year-old posted on social media.
Senegal looked set to progress after Habib Diarra and Ismaila Sarr put them ahead.
Gueye, who scored two goals at the tournament, was replaced shortly after the hour mark, with coach Pape Thiaw sending on Lamine Camara as Senegal sought to protect their advantage.
However, Belgium struck twice in the final four minutes through Romelu Lukaku and Youri Tielemans to send the match into extra time.
Belgium then completed the turnaround when Tielemans converted a penalty awarded after a VAR review involving Senegal substitute Camara.
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