It has already been called the worst flooding in a lifetime by Action Against Hunger regional director Hajir Maalim. Some 273,000 Somalis have had to leave their homes, according to the International Rescue Committee (IRC).
Parts of Kenya and South Sudan have also been hit by the flooding. More than 600,000 people have been forced to leave their homes in South Sudan, IRC says.
Last Wednesday, South Sudan's President Salva Kiir declared a state of emergency.
Humanitarian agencies say things are particularly bad in Pibor, in the east of the country.
"The situation is extreme. The town is now submerged in water completely," Médecins Sans Frontières' emergency coordinator in South Sudan, Edi Ferdinand Atte, told BBC Focus on Africa.
The deputy head of the UN's humanitarian coordination office in South Sudan, Andrea Noyes, said that aid workers are wading through the waters to help flood victims.
"We are having to move around in water up to our knees or up to our thighs to reach people in need," she said.
There is no reliable rainfall data for some of the places thought be impacted the worst.
But figures are available for Kenya, which show that there have been some very high levels of rainfall during October.
On 16 October, the port city of Mombasa recorded more than 100mm (four inches) - that is around the monthly average in one day.
One climate pattern which can cause heavier rains is a weather phenomenon known as a positive Indian Ocean Dipole (IOD), which occurs when the western part of the Indian Ocean becomes significantly warmer than the eastern part.
Whether this is directly attributable to the recent flooding is unclear but it increases the risk of excess rainfall. More heavy rain is expected to hit Somalia , brought in by the depression Kyarr.
The rain is expected to continue throughout the week.
Kyarr has been in the Arabian Sea for around 10 days and at one point became a super cyclonic storm, the first one in the Arabian Sea since 2007, before weakening considerably, BBC Weather says.