The blasts occurred in Sanaa, Hodeidah and other cities, the Iran-backed Shia militias said
The US and UK have begun carrying out strikes on Yemen in the early hours of Friday local time.
The action comes after Washington and London vowed to retaliate against attacks on shipping in the Red Sea and the Gulf of Aden.
The Houthis have pledged support for Gaza during the ongoing fighting between Israel and the Palestinian militant group Hamas. They have been launching drones and missiles at merchant vessels, as well as warships patrolling the vital waterway.