Confirming the figure in a BBC Focus on Africa radio interview, Getachew Reda, a government minister and aide to the prime minister, said: "We are trying to make sure that no-one is affected to such an extent that they lose their lives."
Save the Children said an "emergency response" to deal with the crisis could cost $1.4bn.
"An estimated 400,000 children are now also at risk of developing severe acute malnutrition in 2016, which can lead to stunting, and physical and mental delays in development," it said in a statement.
Several other African states - including Malawi and South Africa - have also been hit by drought.
A famine in Ethiopia in 1984 led to hundreds of thousands of people starving to death.
However, the Ethiopian Embassy in London, in a statement last month, said the country was not at risk of a "famine of any sort, let alone anything remotely like the magnitude of that of 1984".
Ethiopia was also hit by a drought in 2011 and 2008, causing a food crisis.