In a ceremony for the Jewish New Year near Tel Aviv, 47-year-old Saar said he wished to spend more time with his family, including his newborn son.
Prime Minister Benjamin Netanyahu accepted the resignation, Israel Radio reported on Thursday.
The surprise move by the popular politician was described as a "bomb shell" within the Likud.
Saar, who described his decision as a time-out from politics, had been billed as a future candidate for prime minister.
He is married to prominent journalist Geula Even.