Regragui took Morocco to the World Cup semi-final in Qatar in 2022 and was also at the helm in January when Morocco lost in the final of the Africa Cup of Nations but has quit citing exhaustion.
Mohamed Ouahbi will take over as interim coach, reports said. He was in charge when Morocco won the U-20 World Cup in Chile last year.
The 50-year-old Regragui had been the target of supporter criticism despite a stellar record of 36 wins in 49 matches with eight draws and only five losses since taking over in September 2022.
During that time, Morocco recorded the best achievement by an African country at the World Cup and set a new world record for the most successive wins by a national team – a total of 19 between June 2024 and last December.