The Houthis have medium, long-range ballistic missiles in their inventory and they had previously targeted certain strategic locations of Saudi Arabia with armed drones.
He said that these blasts also knocked out the production of 2bn cubic feet of associated gas daily, used to produce 700,000 barrels of natural gas liquids, which will lead to an approximate 50 percent decrease of Ethane and natural gas liquids supply.
The statement said Saudi Aramco, the state-owned oil giant, would provide updated information in the next 48 hours.
President Donald Trump called the Saudi crown prince after the attack, expressing USA support for the kingdom's security and stability.
There were no casualties in the attack but the full extent of the damage was not immediately clear as reporters were not allowed near the plants where Saudi authorities swiftly stepped up security. They raise concerns about the global oil supply and likely will further increase tensions across the Persian Gulf amid an escalating crisis between the United States and Iran over its unraveling nuclear deal with world powers.
"We call on all nations to publicly and unequivocally condemn Iran's attacks", Pompeo said, warning that the Trump administration would work with its allies to make sure Iran was "held accountable for its aggression".
Prince Mohammed had earlier issued a statement saying the kingdom was "willing and able" to respond to this "terrorist aggression", according to Saudi state media.
The UN's Yemen envoy Martin Griffiths said he was "extremely concerned" over the latest attacks, which also drew swift condemnation from Riyadh's Gulf allies, the United Arab Emirates, Bahrain and Kuwait.
Saudi Arabia, leading a Sunni Muslim military coalition that intervened in Yemen in 2015 against the Houthis, has blamed rival Iran for previous attacks, which Tehran denies.
Iran today dismissed as "meaningless" U.S. accusations it was behind drone attacks on Saudi oil installations, suggesting Washington was seeking a pretext to retaliate against the Islamic republic. The attacks likely will further increase tensions across the Persian Gulf amid an escalating crisis between the U.S. and Iran over its unraveling nuclear deal with world powers. The Rapidan Energy Group, a Washington-based advisory group, warned in May that "a successful attack could lead to a monthslong disruption of most Saudi production and almost all spare production".
The mammoth IPO forms the cornerstone of a reform programme envisaged by the powerful crown prince to wean the Saudi economy off its reliance on oil.
Aramco is ready for a two-stage stock market debut including an worldwide listing "very soon", its CEO Amin Nasser told reporters on Tuesday.