Aid groups and the government are calling for help, but fear donor fatigue with other crises worldwide.
A famine in north-east Nigeria, South Sudan, Yemen and Somalia was dubbed the worst humanitarian crisis the world has faced since 1945 by the UN in March.
But Ethiopia is also struggling following successive failed rains.
The government, while better at coping with droughts than in previous years, still does not have the funds to cope by itself.
It allocated $381m (Â£300m) extra over the last two years, but is unable to sustain it for a third year.
It has left Ethiopia in a "dire situation", according to John Aylieff of the World Food Programme, a UN agency.
"We've got food running out nationally at the end of June," he told reporters on Friday.
"That means the 7.8 million people who are in need of humanitarian food assistance in Ethiopia will see that distribution cut abruptly at the end of June."
His words were echoed by John Graham, of Save the Children
He told AFP news agency: "After [the food runs out], we don't know what is going to happen. And without that basic food then you will have problem falling into severe malnutrition because people are not getting any food.
"These children become severely malnourished and that's where you have a very dangerous situation."
Ethiopia will run out of emergency food aid for 7.8 million people affected by drought at the end of this month, the UN has warned.