The warning will be in effect all day on, the meteorological service said as heavy rains and possible thunderstorms are expected.
In a statement on Thursday morning, Paphos police said that the rain caused landslides on the Kelokedara-Salamiou Road and the Arminou-Filousas Road.
They warned drivers to be especially careful, as the road can be slippery and there could be minor flooding in areas.
Police also cautioned drivers on the Limassol-Paphos motorway, saying that the intense rain is causing low visibility conditions.
Drivers in Troodos should use caution as the roads are slippery due to snowfall. Police said the Kakopetria-Troodos Road and the Platres-Troodos roads are especially slippery.
The rain is expected to continue into the evening, and scattered showers and storms are expected on Friday, the meteorological service said.