Yemen has appealed to the World Health Organisation and the US Centre for Disease Control in Atlanta for help.
Yemen's Health Minister, Abdelwali Nasher, said teams of doctors had been rushed to the affected area - a remote part of Yemen near the Saudi border.
About half of all livestock in the Wadi Moor area in Al-Hudaydah province are said to have died.
Yemen has appealed to the World Health Organisation and the US Centre for Disease Control in Atlanta for help.
Mr Nasher told the BBC that at least 17 people had died from the fever, but another Yemeni Health Ministry official put the death toll as high as 77.
Insecticide
Mr Nasher said Saudi Arabia would soon be sending planes across the border to spray insecticide to kill the mosquitoes which are thought to be spreading the disease.
At least 16 people died from Rift Valley Fever in Saudi Arabia last week, in the first outbreak of the viral disease outside Africa.
It usually affects livestock, but can be spread to humans by mosquitoes or contact with infected animals. The fever can lead to victims suffering swollen brains and burst arteries.
The BBC's Middle East correspondent Frank Gardner says the hot, damp climate found on Saudi Arabia and Yemen's Red Sea coasts is an ideal breeding-ground for mosquitoes.
Saudi Arabia has since banned the import of livestock from several African countries as well as from Yemen.
The disease was first reported on 11 September in Saudi Arabia's Jizan province, bordering on Yemen.
Sheep
Saudi Arabia has banned the movement of livestock in and out of Jizan, to contain the fever.
The fever is believed to have been introduced to Saudi Arabia via sheep, a large number of which have recently died in Jizan.
Since Rift Valley Fever was first identified in 1930, after an epidemic among sheep in Kenya, it has also affected Egypt, Madagascar, Mauritania and Somalia, according to the World Health Organisation.