The strike on Sunday marked the deadliest reported since clashes between members of the Ethiopian army and a local militia known as Fano erupted in towns and cities across Amhara after months of tensions.
"Twenty-two bodies were brought to the hospital, while four others who were critically injured died soon after arriving in the hospital" in Finote Selam, said the hospital official.
"We've so far received 55 injured patients out of which more than 40 are gravely injured," he added, speaking anonymously over safety concerns.
Tikikil Kumlachew, a university teacher who was visiting a relative in the hospital from an unrelated incident, said he had seen 14 bodies there and been told by a medical worker that another 12 had died.
"The explosion shook the city. I don't know if it was a drone or something else. But it fell from the sky," he said.
A resident who arrived shortly after the strike told AFP he had "helped in the burial of bodies of 30 victims."
He said he saw "a medium sized freight vehicle had been completely destroyed in an air strike with dead bodies strewn around the vehicle."
Prime Minister Abiy Ahmed's government imposed a six-month state of emergency across Amhara on August 4 and several cities remain under curfew, although violence eased towards the end of last week.
The unrest has revived fears about the stability of Africa's second most populous country, seven months after a peace deal ended a brutal two-year conflict in the neighboring region of Tigray.
Federal forces managed late last week to push Fano militiamen out of most major towns in Amhara, but clashes continue in other parts of the region, the Ethiopian Human Rights Commission, EHRC, said in a statement.
The fighting, which has been fueled by Fano accusations that the federal government is trying to weaken Amhara's defenses, is Ethiopia's biggest security crisis since a two-year civil war in the northern Tigray region ended last November.
Ethiopia's government denies the allegations by Fano, an informal militia that backed federal forces during the Tigray war. Spokespeople for the government, the military and Prime Minister Abiy Ahmed did not respond to requests for comment on Monday about the suspected air strike or EHRC's statement.
In its statement on Monday, the EHRC said it had received credible reports that strikes and shelling in Finote Selam and other towns had resulted in civilian casualties, without specifying when these events occurred.
EHRC's statement said its investigators had documented a variety of incidents since the conflict started, including the killing of protesters who blocked roads, the looting of weapons and ammunition from police stations and prisons, and the targeting of Amhara regional administration officials.
In Amhara's capital Bahir Dar, civilians were killed on the streets or outside their houses, EHRC said, adding there were credible reports of "many civilian casualties" in Gondar, the region's second biggest city, and extra-judicial killings by security forces in Shewa Robit.
In Addis Ababa, the capital, there have also been widespread arrests of civilians of ethnic Amhara origin, it said.
Information for this report came from Reuters and AFP.