"The Yemeni Armed Forces confirm that they will respond to this blatant aggression," the Houthis said in a statement.
The movement said that the Israeli attack had targeted a power station, the Hudaydah port and fuel tanks, adding that those were civilian targets.
The Houthis also vowed to continue operations in support of the Gaza Strip.
Earlier in the day, the Israel Defense Forces claimed responsibility for a series of airstrikes on Hudaydah, calling the strikes a response to attacks carried out against Israel. Israeli Prime Minister Benjamin Netanyahu said the attacked port had been used for military purposes, including importing weapons from Iran.