The department explained that rainfall will not only increase in strength but also cover a wider area than before.
This means some places that have not been receiving much rain could start experiencing downpours during the week.
Residents in the listed regions have been advised to stay alert and follow weather updates closely.
People living in low-lying areas have been asked to be especially careful because of the risk of flooding.
Heavy rains can quickly fill rivers and streams, causing them to overflow. Roads in some areas may also become impassable due to water or mud.
Motorists have been urged to drive carefully during heavy downpours, as visibility may be poor and roads slippery.
Farmers in the affected regions are likely to welcome the rains, especially those who have already prepared their land for planting.
However, the department cautioned that too much rain within a short period can also damage crops and wash away topsoil.
It encouraged farmers to take necessary steps to protect their farms where possible.
While many parts of the country will be receiving rain, some regions will continue to experience high daytime temperatures.
The Coast, South-eastern Lowlands, North-eastern and North-western Kenya are expected to record maximum temperatures above 30 degrees Celsius.
This means residents in these areas may experience hot and humid conditions during the day, even as some parts receive rainfall.
The weatherman advised people to stay hydrated, especially in hot areas, and to avoid staying under direct sunlight for long hours.
For those in rainy regions, carrying umbrellas and wearing protective clothing may help reduce exposure to cold and wet conditions.
The weather department said it will continue to monitor the situation and provide updates if there are any significant changes.
Kenyans have been encouraged to rely on official forecasts and avoid spreading unverified information.