The 27-year-old revealed his decision on social media shortly after Senegal threw away a two-goal lead to lose 3-2 to Belgium after extra time in their Round of 16 clash.
Writing in French, Gueye said he would speak further about the team's elimination at a later date but made it clear he would not represent Senegal under the current technical crew.
"I'll come back to speak about our elimination, but today I announce that as long as this technical staff remains, I will take a break from the national team," he wrote.
Senegal appeared on course for the quarter-finals after first-half goals from Habib Diarra and Ismaïla Sarr gave the African champions a commanding 2-0 lead.
However, Belgium mounted a remarkable comeback as Romelu Lukaku and Youri Tielemans scored late to force extra time before Tielemans converted a 125th-minute penalty, awarded after a VAR review, to seal a dramatic 3-2 victory.
The defeat ended Senegal's hopes of reaching the World Cup quarter-finals for the first time since their memorable debut campaign in 2002.
Gueye's announcement has intensified pressure on Thiaw, whose substitutions while protecting a two-goal advantage have come under heavy criticism from supporters and analysts.
Defending his decisions after the match, Thiaw insisted the changes were forced by player fatigue rather than tactical considerations.
"They were tired and couldn't continue. Leaving them on the field would have been unprofessional on our part. We had to replace them like for like," he said.
"Of course, when you lose a match after leading 2-0, people will talk about the substitutions. But you can't reduce everything to that. These changes were dictated primarily by fatigue rather than tactical considerations."
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