The blaze, blamed on an electrical fault, hit the Abu Sifin church in densely populated Imbaba west of the Nile river, part of Giza governorate.
Witnesses described panicked scenes as people rushed into the multi-storey house of worship to rescue those trapped but were soon overwhelmed by the heat and deadly smoke.
The interior ministry said "forensic evidence revealed that the blaze broke out in an air-conditioning unit on the second floor of the church building" which also houses social services.
Father Farid Fahmy, of another nearby church in Imbaba, told AFP the fire was caused by a short circuit.
"The power was out and they were using a generator," he said. "When the power came back, it caused an overload."
"Everyone was carrying kids out of the building," said Ahmed Reda Baioumy, who lives next to the church. "But the fire was getting bigger and you could only go in once or you would asphyxiate."
The Egyptian Coptic Church and the health ministry reported 41 dead and 14 injured in the blaze before emergency services said they had brought the blaze under control.
The grand imam of Al-Azhar, Egypt's foremost Muslim institution, expressed his condolences for "the tragic accident" and affirmed "the readiness of Al-Azhar hospitals to receive the injured".
President Abdel Fattah al-Sisi declared on his Facebook page in the morning: "I have mobilized all state services to ensure that all measures are taken."
He later said he had "presented his condolences by phone" to Pope Tawadros II, who has been the head of the Coptic Orthodox Church since 2012.
The Giza governor ordered "urgent aid of 50,000 pounds (around $2,600) for the families of the deceased and 10,000 pounds for the injured."
Copts are the largest Christian community in the Middle East, making up at least 10 million of Egypt's 103 million people.