Family and friends of a young couple had hired the boat for an engagement party and were sailing north of Cairo hit was hit, according to eyewitnesses.
An Interior Ministry statement said 15 bodies had been found and six people were still missing.
The captain of the cargo boat has been arrested. Five people were rescued, but at least two children died.
It is not clear if the couple thought to be celebrating their engagement were among the dead, said AFP news agency.
Traffic had been heavy along the Nile, where many Egyptians had been celebrating the end of the holy month of Ramadan.
At least 15 people have been killed in a crash between a cargo vessel and a passenger boat on Egypt's River Nile.