The coalition, which has been fighting the Houthis in Yemen for more than a decade, said air defences had intercepted ballistic and cruise missiles fired by the rebel group towards Saudi Arabia's capital Riyadh, the oil-rich Eastern Province and the southern region.
A building in Riyadh belonging to the Saudi oil giant Aramco sustained "minor" damage on Sunday caused by falling debris from an interception, the Saudi energy ministry said.
The attempted attack did not result in any casualties.
The Houthis have recently stepped up attacks on neighbouring Saudi Arabia, with airports and oil facilities in the kingdom among the main targets.
Saudi Arabia backs Yemen's internationally recognised government and is leading a military coalition fighting the Houthi rebels.
On Saturday, the Houthis claimed a string of missile and drone attacks deep into the Saudi territory.
The reported strikes targeted the main airport in Riyadh and Aramco facilities, as well as a military camp in Najran in southwestern Saudi Arabia.
A Houthi military spokesman said the "successful" operations were in response to deadly Saudi attacks earlier this week against civilians in Yemeni areas under the group's control, including the capital Sanaa.
The death toll in an air bombardment in Sanaa, allegedly conducted by Saudi warplanes on Saturday, rose to 33 people, including 13 children, according to a Houthi health official.
The strikes on residential buildings in the Bani Hushaysh district in Sanaa also left 39 others injured, the Houthi-run health ministry said, according to the Yemeni news agency Saba.
Initially, the group said the attack left 25 dead and 30 others injured.
So far, there has been no comment from the Saudi-led coalition.
The years-long conflict in Yemen has recently intensified again amid the wider war involving the United States and Iran.
Even before the flare-up of fighting, the impoverished country was home to one of the world's worst humanitarian crises.
