An updated tally sent to AFP by Faly Aritiana Fabien, a senior official at Madagascar's National Risk Management Office, showed two more deaths in addition to the previously announced 16.
Another 19 people are missing after the storm flooded several districts and cut roads linking them to the capital Antananarivo.
In a statement, the office said more than 55,400 people had been affected, more than half of whom were displaced from their homes.
Storm Cheneso made landfall on January 19, packing winds of up to 110 kilometers per hour and triggering downpours.
It is the first tropical storm of the current cyclone season in southern Africa, which typically runs from November to April.