Azzan al-Qumeiri, member of the local emergency committee, said three bodies were recovered on Saturday as they had been washed away by floods in different places in provincial capital Al-Ghayza.
Emergency teams are currently searching for 25 other people, who went missing since the beginning of the weather storm.
Mahra has been pounded by high winds and torrential rains since Sunday, after Cyclone Luban formed in the Arabian Sea off the coast of Oman earlier this month.
About 3,800 families have been displaced in Mahra since Sunday.
It is the fifth time that Yemen has been struck by tropical storms since 2015.