The Aramco Tower, a skyscraper in the Saudi Arabian capital's central financial district, had been hit by an air attack.
A statement issued via the Houthi-controlled Saba news agency confirmed the group had targeted Riyadh's business zone on Saturday, without mentioning the Aramco Tower by name.
The Saudi energy ministry said the tower had suffered only "minor damage" and no one had been killed or injured.
Footage authenticated by BBC Verify shows more extensive damage to the building, with at least one floor appearing to have been badly hit by a missile or drone strike.
Windows on more than one level appear to have been shattered by the strike.
The Houthis also said Riyadh's airport and Aramco oil storage facilities were targeted in separate strikes. Saudi Arabia said its air defences had intercepted and destroyed several missiles.
The strikes were the latest claimed by the Yemen-based armed group against targets deep inside Saudi Arabia, which the Gulf power has struggled to contain in recent months.
It came a day after the Houthis accused a Saudi-led coalition of killing at least ٣٣ people , including women and children, in an air strike on Yemen.
Footage broadcast by Houthi-run television channel Al Masirah showed rescuers pulling bodies from the rubble of several buildings in al-Shariyah, a town to the east of the capital, Sanaa.
Saba said ٣٩ people had been injured in the strike. Saudi Arabia has not commented.
A Saudi-led coalition has been fighting the Houthis for more than a decade in support of Yemen's internationally recognised government, which has lost control of a large swathe of the country to the rebel group.
Although the conflict had largely been dormant in recent years, fighting has intensified following the outbreak of the Iran war.
An informal ceasefire unravelled in July after the Tehran-backed Houthis announced a "maritime embargo" against Saudi Arabia and began missile and drone attacks on Saudi airports, oil facilities and tankers in the Red Sea.
The Houthis said they were retaliating for what they have called a Saudi blockade of their territory, as well as an air strike on Sanaa airport Saudi Arabia said had been to prevent an Iranian aircraft from landing there.
Major fighting has since resumed between Houthi forces and troops aligned with Yemen's Saudi-backed government.
The United Nations says more than ١,٦٠٠ people have been killed and more than ٣٠٠,٠٠٠ displaced since fighting resumed.
سلطات قالت إن زولين اتقتلوا في هجوم حوثي على مطار في شرق السعودية
أمريكا أمرت بعض الدبلوماسيين يغادروا السعودية مع تصعيد هجمات الحوثيين
صاروخ حوثي ضرب مبنى أرامكو بعد ضربة التحالف بقيادة السعودية على مخزن وقود في اليمن
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