The strikes on the country's main air gateway came just hours after UN workers were evacuated following deadly fighting that has sent tensions between Tehran and other Middle East powers soaring.
Yemen's President Abedrabbo Mansour Hadi has urged his Arab allies to keep up the bombing raids until the Huthi Shiite rebels surrender, branding them Iran's "puppet".
The Huthis and allied rebel military units have overrun much of the country and prompted Hadi to flee what had been his last remaining refuge in the main southern city Aden for Saudi Arabia.
Witnesses on Sunday reported hearing three loud explosions and seeing a large fire when Sanaa International Airport was bombed at around midnight.
"This was the first time they hit the runway" since the campaign began, an aviation source said. "The airport is completely out of service."
More than 200 staff from the UN, foreign embassies and other organisations had been flown out from the airport on Saturday.
Pakistan said it was preparing to evacuate its citizens and diplomatic staff from Hudaida in western Yemen.
Overnight air strikes hit the headquarters of the rebel republican guard at Al-Subaha base in Sanaa, killing 15 soldiers, a military official said.
The Huthis are backed by army units loyal to former president Ali Abdullah Saleh, who stepped down in 2012 after a year-long popular uprising and is accused of supporting the rebels.
In a televised speech Saturday, Saleh urged the Arab League to help end the crisis "peacefully", saying the "problem will not be solved with strikes".
The 22-member League was holding a second day of top-level talks Sunday in Egypt where leaders were expected to approve the creation of a joint military force.
The Saudi-led strikes also targeted an airbase in rebel-held Hudaida, witnesses said.
Other raids targeted a base of the First Artillery Brigade in Saada, the northern stronghold of the Huthis.
The Sunni Arab coalition is said to have been spurred into action by the prospect of an Iranian-backed regime seizing power in impoverished Yemen, wedged on the southern tip of the Arabian Peninsula.
The fighting has cast a shadow over crunch talks between world powers and Iran aimed at ensuring Tehran never develops an atomic bomb.
Russia's chief negotiator in the nuclear talks said Moscow hoped the Yemen conflict would not jeopardise the talks between Iran and world powers under way in Switzerland.
"Unfortunately, we are seeing that the tragedy that is happening in this country (Yemen) is having an impact on the atmosphere of the negotiations," said deputy foreign minister Sergei Ryabkov.
"We hope that the situation in Yemen will not bring about a change in the position of certain participants."
According to Saudi Arabia, more than 10 countries have joined the coalition defending Hadi. Washington and Britain have pledged logistical support.
Hadi had gone into hiding earlier in the week as rebels advanced on Aden and a warplane attacked the presidential palace there.
He surfaced in Riyadh Thursday before heading to the Egypt summit.
Late Saturday, anti-Huthi local fighters were reported to have taken full control of Aden airport with the loss of five men, and nine killed on the rebel side.
The rebels also set up a base in Dar Saad on the city's northern fringe after clashes in which six people, including four Huthis, were killed, a military source said.
Dozens of people have died in Aden in recent days in fighting between the rebels and local anti-Huthi militia.
Fourteen charred bodies were pulled from an arms depot in a cave near the port city after a series of massive blasts with more victims feared to be inside.
The cause was not immediately clear, but residents had been looting the arsenal of Soviet-era weapons, apparently to defend themselves as the city slides into chaos.
Gulf diplomats said the bombing could last up to six months, and accused Iran of providing "logistical and military support" to the rebels.
They said Riyadh and its allies had decided to intervene after satellite imagery in late January showed the movement of Scud missiles north towards the Saudi border, with the capacity to strike a large part of the kingdom's territory.
A coalition spokesman told reporters Saturday that "most" of the Huthis' missile capabilities were believed to have been destroyed in the air strikes.