Huthi-controlled Al-Masirah TV said a port worker and three engineers were killed with 33 wounded in an "initial toll", adding ambulance and rescue teams were still searching for missing people.
The Israeli military said it was striking several Huthi rebel targets in Yemen, including power stations and a seaport.
The strikes came a day after the rebels said they targeted Israel's Ben Gurion Airport with a missile.
"In a large-scale air operation today, dozens of Air Force aircraft, including fighter jets, refuelling planes, and reconnaissance aircraft, attacked military-use targets of the Huthi terrorist regime in the Ras Issa and Hodeida areas of Yemen," military spokesman Captain David Avraham said in a statement to AFP.
"The IDF (military) targeted power stations and a seaport used for oil imports," a military statement said.
In July Israel also hit Hodeida port, causing what a port official said was at least $20 million in damage, after a Huthi drone strike penetrated Israel's air defences and killed a civilian in Tel Aviv.
Hodeida is a key entry point for fuel and humanitarian aid to war-ravaged Yemen.
The sites targeted Sunday were used by the Huthis, who seized the Yemeni capital Sanaa in 2014, to "transfer Iranian weaponry to the region and supplies for military needs", the statement said.
"The strike was carried out in response to recent attacks by the Huthi regime against the state of Israel," it added, after the rebels said they tried to hit Ben Gurion as Prime Minister Benjamin Netanyahu arrived back from New York.
Earlier Sunday the military said an "unmanned aerial target" approaching Israel over the Red Sea -- where the Huthis have regularly launched attacks on shipping -- had been intercepted.
Israel's Defence Minister Yoav Gallant said "no place is too far" for the Israeli military to strike its enemies, after he monitored the operation from an air force command and control room about 2,000 kilometres (1,300 miles) from Yemen.
Since November the Huthis have targeted Israel and its perceived interests in stated solidarity with Palestinians in Gaza, launching dozens of missile and drone strikes that have disrupted global shipping through vital waterways off Yemen.
In a statement, Hamas condemned the Israeli attack, calling it "an extension of the occupation's crimes in Palestine, Lebanon, and the Arab region, with blatant and open US support".
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