The air strike in the town of Adi Daero appears to be one of the deadliest carried out during the nearly two-year war, which has killed thousands and uprooted millions.
The school was on a list of sites housing internally displaced persons (IDPs) that the Office of the United Nations Resident and Humanitarian Coordinator in Ethiopia sent to Ethiopia's foreign ministry in January, according to one of the aid workers and two UN sources.
A range of Ethiopian government and military officials did not respond to Reuters requests for comment on the air strike or the letter.
The government has previously denied targeting civilians in the conflict.
The UN co-ordinator's office also did not respond to requests for comment.
Reuters could not independently verify details of the air strike or the death toll.
Most communications have been down for over a year in Tigray, where the federal government has been battling regional forces since November 2020.
But four humanitarian sources, who asked not to be named because they were not authorised to speak to the media, said that the school had been hit, citing eyewitnesses and local administrative officials.
Survivors of the strike told humanitarian workers after fleeing to the town of Shire, about 25km away, that at least 50 people had been killed and more than 70 injured, an aid worker in Shire told Reuters.
The survivors said they had heard what sounded like a drone, this aid worker said.
Another aid worker, who was briefed on the death toll by colleagues, said 62 people had been killed.
This person did not have information about the number of people wounded.
The two other humanitarian sources, both from the UN, had no information about the number of casualties.
The Tigray external relations office said in a statement that 65 people had been killed and 70 injured in the strike.
It blamed the Ethiopian and Eritrean governments for what it called a "massacre".
Eritean troops have fought on the side of Ethiopia's federal government during the conflict.
The deadliest previous air strike of the war occurred in January, when 59 people were killed at a displaced persons camp in the northwestern town of Dedebit, according to the UN human rights office.
