Ambassador Adel al-Jubeir says the operations began at 7 p.m. Eastern time.
He says the Houthis, widely believed to be backed by Iran, "have always chosen the path of violence." He declined to say whether the Saudi campaign involved U.S. intelligence assistance.
Al-Jubeir made the announcement at a rare news conference by the Sunni kingdom.
He says the Saudis "will do anything necessary" to protect the people of Yemen and "the legitimate government of Yemen."
The departure of Yemeni President Abed Rabbo Mansour Hadi illustrated how one of the most important American counterterrorism efforts has disintegrated.