"I condemn these destructions and I call on all parties to keep cultural heritage out of the conflict," said UNESCO director general Irina Bokova.
A Saudi-led coalition has intensified strikes on the Iran-backed rebels in the capital and their northern stronghold of Saada in its efforts to restore the crumbling authority of exiled President Abedrabbo Mansour Hadi.
Bokova said the bombing had caused severe damage to many historic buildings in the Yemeni capital, while the old city of Saada and the archaeological site of the pre-Islamic walled city of Baraqish, had also suffered damages.
Sanaa's old city, situated in a mountain valley, has been inhabited for over 2,500 years and was a major centre for the propagation of Islam, boasting over 100 mosques, 14 hammams and over 6,000 houses built before the 11th century.
It was inscribed on UNESCO's World Heritage List in 1986.