Bounou, also known as Bono, was named in the starting line-up and lined up with his teammates for the singing of the national anthem on Sunday but was then seen in a lengthy discussion with referee Cesar Ramos of Mexico.
Munir El Kajoui (33) then appeared for the team photo before kick-off and took Bounou's place as the game at the Al Thumama Stadium got underway.
Images from the stadium showed Bounou slumped over with his hands braced on his knees.
"He felt dizzy and I spoke with coach (Walid) Regragui about withdrawing him from the starting lineup," Hefti told Moroccan state television Arryadia. "But he is fine now and he will play against Canada."
Morocco beat Belgium 2-0 with goals from Romain Saiss (32) and Zakaria Aboukhlal to go top of group F with four points, before Sunday's late game between Croatia and Canada.