Thousands of people attended the colorful Epiphany celebration known as Timkat in the northern city of Gondar.
"Ten people have lost their lives," the Ethiopian Press Agency quoted the city's police chief, Ayalew Teklu, as saying. "Thirteen people have sustained serious injuries, including four members of the security services."
Ashenafi Tazebew with Gondar University Hospital said more than 250 people had received medical care. Some 80 people remained at the hospital, Ashenafi said.
The collapse occurred inside the Emperor Fasilides Bath in the city where several thousand Ethiopians and tourists attended the celebration commemorating the baptism of Jesus.
The Ethiopian News Agency reported that more than 15,000 foreigners attended the event in Gondar.
UNESCO late last year added Ethiopia's Epiphany festivities to its list of Intangible Cultural Heritage of Humanity, which attracted more attendees.