The bus carrying about 70 passengers was traveling from the city of Minya, south of Cairo, on Sunday when it swerved from a narrow road and plunged into an irrigation canal.
Many of the passengers drowned before rescue workers arrived at the scene. Several others died later in hospital from their injuries, MENA said.
Local officials said the bus swerved to avoid a collision with an oncoming truck. Eyewitnesses said the bus driver was driving too fast.
According to media reports, the victims and those injured in the accident were locals and also university students.
Road accidents are frequent in Egypt largely due to reckless driving and poor roads.
According to the Egyptian Interior Ministry, about 27,000 road accidents occur in the North African country every year, killing over 6,000 people and injuring another 30,000.