A state of emergency has been declared in the Central American nations, where more than 20 people are missing.
It has caused heavy rains, landslides and floods which are blocking roads, destroying bridges and damaging houses.
In Costa Rica, nearly 400,000 people are without running water and thousands are sleeping in shelters.
At least six people have died in the storm there, while another 11 were killed when it moved north and reached Nicaragua.
Three people have been killed in Honduras and several are reported missing.