Rescue teams have recovered 14 bodies and were searching for survivors in the Kafr al-Sheikh province north of Cairo, the agency reported, adding that 17 people were believed to have been on board.
The provincial governor Al-Sayed Nasr told AFP that the boat, which was not licensed to work as a ferry, had been too small to accommodate the passengers.
The accident came months after at least 36 Egyptians were killed when a party boat collided with a cargo ship in the Nile.
Egypt Nile boat crash death toll rises to 36
Following that accident in July, the government pledged to "achieve discipline" on the waterway.
It banned use of loud speakers on vessels hired for private ceremonies and on ferries transporting people. The cabinet also decided not to build new berths along the river.
The Nile, which runs along the length of Egypt, is dotted with cargo ships, party boats and fishing vessels.
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