Attempts to get medical supplies and relief aid to the region have been hampered as some villages are still cut off.
Wells, roads and farms have also been destroyed and power lines remain cut.
Among the affected areas is the Unesco world heritage site of Shibam, where historic mud-brick buildings are threatened with collapse.
Shibam, which was isolated by the flood waters, is home to more than 20,000 people and is famous for its ancient highrise buildings that have given the town the nickname "the Manhattan of the desert".
A cargo vessel also ran aground off the port of Nashtun in Mahra, but all 17 crew members were rescued.
Yemen is one of the poorest countries in the world and its government is already struggling to contain an uprising in the north, unrest in the south and the re-emergence of al-Qaeda in the region.