A stark warning issued by the UN's humanitarian office, Ocha, said the malnutrition situation is "alarming".
It added that nearly one million Somalis, one in 12 of the population, "struggle... to meet their food needs".
The drought in Somalia has been partly caused by the El Nino weather phenomenon which has affected east and southern Africa.
Africa Live: BBC news updates
Does Ethiopia need aid to cope with drought?
The worst-affected areas of the country are parts of Puntland and the self-declared republic of Somaliland.
Many of those in need of help are people who have been displaced by years of conflict in the country.
In all 4.7 million people, nearly 40% of the population, need some sort of humanitarian assistance.
As the drought is intensifying there "many more people risk relapsing into crisis,"  said the UN's Humanitarian Coordinator in Somalia Peter de Clercq.
Highlighting the condition of the children, he said that 58,300 will die "if they are not treated".
Mr de Clercq appealed for more funds so they can be helped quickly.
In neighbouring Ethiopia more than 10 million people need food assistance following the failure of the rains.
And Zimbabwe has declared a state of disaster in some drought-affected areas of the country.
More than 50,000 children in Somalia "face death" because of the ongoing drought there, the UN says.