The dredger sank early morning on Wednesday near al-Ismailiya, north east of the Egyptian capital.
Forty five sailors were on board the vessel Khattab when the incident occurred.
Besides the two crew members who drowned, the two missing crew are feared dead.
The other sailors were all rescued, including six who were injured in the accident.
Aljazeera’s correspondent in Cairo said the dredger’s driver was seriously injured.
A Canal Authority official said a technical fault was the apparent cause of the sinking.
Egypt has been hit by a series of major transport disasters in recent months.
More than 1,000 people had died when a ferry sank in the middle of the Red Sea in February, in one of the worst maritime tragedies in recent years.
Last month, 58 people were killed in the Nile Delta town of Qalyub when two commuter trains collided in Egypt’s worst railway accident in four years.
A day later, 11 Arab-Israeli tourists were killed in a bus accident in the Sinai peninsula.