"The interception resulted in the projection of fragments throughout some residential areas, which caused the martyrdom of a Yemeni resident, and injuries among 11 civilians," Turki Al-Malki was quoted as saying by the Saudi state news agency SPA.
The spokesman said that the missile had been downed by the Royal Saudi Air Defense. He also accused Iran of supporting the Houthis in Yemen and "providing them with advanced capabilities."
He stressed that ballistic missiles launches at densely-populated civilian areas were "a direct breach of the principles of the international humanitarian law."
Al-Malki stressed that the coalition would respond with "all deterring measures" in conformity with international humanitarian law and bring those responsible to account.
Earlier, local media reported that Saudi air defense forces intercepted and destroyed a ballistic missile fired by the Houthis from Yemen into the south of the Arab kingdom's territory.
Yemen has been engulfed in a violent conflict between the government and the Houthis. Since March 2015, the Saudi-led coalition of mostly Gulf countries has been carrying out airstrikes against the Houthis at the Yemeni government's request. The rebel movement has repeatedly launched missiles from Yemeni territory targeting different cities in Saudi Arabia in the course of the conflict.