Officials and meteorologists say the storm is the most intense in decades in the arid country, whose storm response is hampered by poverty and a raging civil war.
In the provincial capital Mukalla, whose 300,000 people are largely ruled by al Qaeda fighters since the army withdrew in April, water submerged cars on city streets and caused dozens of families to flee to a hospital for fear of rock slides.
Residents said the seafront promenade and many homes had been destroyed by the cyclone, called Chapala, and officials in the dry hinterland province of Shabwa said about 6,000 people had moved to higher ground.
“The wind knocked out power completely in the city and people were terrified. Some residents had to leave their homes and escape to higher areas where flooding was less; it was a difficult night but it passed off peacefully,” said Sabri Saleem, who lives in Mukalla.
There were no initial reports of injuries.
An al Qaeda militant on Twitter prayed for deliverance from the storm and said that a U.S. pilotless drone was flying especially low over the city, where the militant group’s deputy leader was killed in an air strike in June.
“May God cause it to crash,” said the man, going by the name of Laith al-Mukalla.
“God spare us your wrath, and place the rains in heart of the valleys and mountains.”
The cyclone first hit the remote Yemeni island of Socotra, killing three people and displacing thousands.
An island of natural beauty, Socotra is home to hundreds of plant species found nowhere else on Earth and lies 380 km (238 miles) off Yemen in the Arabian Sea. Its 50,000 residents speak their own language.
Meteorological agencies predicted Chapala would hit land around Balhaf, site of Yemen’s liquefied natural gas terminal, and weakening as it advanced towards the capital Sanaa in the country’s north.
The facility has been mostly shuttered since the start of a war in March between a Saudi-led Arab military coalition and the Iran-allied Houthi movement which controls Sanaa.
It was not immediately clear if the terminal, once a lifeline for Yemen’s weak economy, suffered damage.
(Reporting By Mohammed Ghobari and Noah Browning, Editing by Angus MacSwan)