Uhuru Kenyatta appealed for international aid and said the government would increase food handouts to the most needy communities.
Kenya's Red Cross says 2.7 million people face starvation if more help is not provided.
Other countries in the region have also been hit by the drought, blamed on last year's El Nino weather phenomenon.
In Somalia, nearly half the population is suffering from food shortages and the UN says there is a risk of famine in several parts of the country.
During the last drought on this scale in 2011, famine killed about 250,000 Somalis.
In a statement, Mr Kenyatta said the government had allocated $105m (Â£84m) to tackle the drought which has affected people, livestock and wildlife in 23 of Kenya's 47 counties.
"Support from our partners would complement government's efforts in mitigating the effects of drought," he said.
Mr Kenyatta added that all purchases of food and other items would be made in a transparent way.
"I will not tolerate anybody who would try to take advantage of this situation to defraud public funds," the president said.
Kenya's president has declared the drought, which has affected as much as half the country, a national disaster.