CAIRO—At least five people suffered minor injuries early Wednesday when four bombs exploded at three metro stations in Cairo during the crowded morning rush hour, state media reported, breaking a period of relative calm that preceded the election of Egypt's new president.

According to Egypt's flagship state newspaper, Al Ahram, the homemade explosives detonated at subway stations in central and northern Cairo within the same hour as commuters began heading to work. Security officials quoted by the newspaper said the explosions...