The strikes are the latest in over a year of direct attacks and counterstrikes between Israel and Houthi militants in Yemen, part of a spillover from the war in Gaza.
The Israeli military said the targets included a military compound housing the presidential palace, two power plants and a fuel storage site.
"The strikes were conducted in response to repeated attacks by the Houthi terrorist regime against the State of Israel and its civilians, including the launching of surface-to-surface missiles and UAVs toward Israeli territory in recent days," the Israeli military said in a statement.
On Friday, the Houthis said they had fired a ballistic missile towards Israel in their latest attack, which they said was in support of Palestinians in Gaza. An Israeli Air Force official said on Sunday the missile most likely carried several sub-munitions "intended to be detonated upon impact."
"This is the first time that this kind of missile has been launched from Yemen," the official said.
Abdul Qader al-Murtada, a senior Houthi official, said the Houthis, who control much of Yemen's population, would continue to act in solidarity with Palestinians in Gaza.
"(Israel) must know that we will not abandon our brothers in Gaza, whatever the sacrifices," he said on X.
Sanaa residents told The Associated Press they heard explosions close to a closed military academy and the presidential palace.
They saw plumes of smoke near Sabeen Square, a central gathering place in the capital.
"The sounds of explosions were very strong," said Hussein Mohamed, who lives close to the presidential palace.
Ahmed al-Mekhlafy said he felt the sheer force of the strikes.
"The house was rocked, and the windows were shattered," he told AP.
The Israeli strikes were the first to hit Yemen since a week ago, when Israel said it targeted energy infrastructure it believed was used by the rebels.
The latest strikes follow the Houthis' claim of launching a newly equipped missile toward Israel on Friday, targeting the country's largest airport, Ben Gurion.
Defence Minister Israel Katz said in a statement that Israel continues to "impose an air and naval blockade," without details.
Yemen's rebel group is "learning the hard way that it will pay and is paying a heavy price for its aggression against the State of Israel," Prime Minister Benjamin Netanyahu said in televised remarks.
Houthi attacks over the past two years have up-ended shipping in the Red Sea, through which about $US1 trillion ($A1.5 trillion) of global goods passes each year.
Since Israel's war in Gaza against the Palestinian militant group Hamas began in October 2023, the Iran-aligned Houthis have attacked vessels in the Red Sea in what they describe as acts of solidarity with the Palestinians.
From November 2023 to December 2024, the Houthis targeted more than 100 commercial and naval ships with missiles and drones.
They have also frequently fired missiles towards Israel, most of which have been intercepted. Israel has responded with strikes on Houthi-controlled areas of Yemen, including the vital Hodeidah port.
with Reuters
