March 24, 2017 0200 GMT
People are already starving to death in all four countries, and the World Food Programme said more than 20 million lives are at risk in the next six months.
"Time is running out for more than a million children," UNICEF Executive Director Anthony Lake said in statement, Reuters reported.
"We can still save many lives. The severe malnutrition and looming famine are largely manmade. Our common humanity demands faster action. We must not repeat the tragedy of the 2011 famine in the Horn of Africa."
Famine was formally declared on Monday in parts of South Sudan, which has been mired in civil war since 2013. The conflict has increasingly split the country along ethnic lines, leading the United Nations to warn of a potential genocide.
UNICEF said 270,000 children in South Sudan were severely malnourished. Save the Children, a charity, said on Monday that more than one million children in South Sudan were at risk of starving.
South Sudan has also been hit by the same East African drought that has pushed Somalia back to the brink of famine, six years after 260,000 people starved to death in 2011.
UNICEF said 185,000 children were expected to suffer from severe acute malnutrition in Somalia this year, but the figure was likely to rise to 270,000 in the next few months.
Another 462,000 children are suffering from severe acute malnutrition in Yemen, where two years of war, launched by Saudi Arabia and its Arab allies, have caused economic collapse and severe restrictions on shipping.
Famine has been ongoing since last year in parts of northeastern Nigeria, where the government is fighting the terror group Boko Haram. The number of children with severe acute malnutrition is expected to reach 450,000 this year, UNICEF said.
UN Security Council ambassadors are due to travel to northern Nigeria, Cameroon, Chad and Niger next month to draw international attention to the humanitarian crisis triggered by Boko Haram.