A search and rescue plane spotted a lifeboat near where the 6,600-tonne Al Salam 89 last had contact with shore at about 10 p.m. (2000 GMT) on Thursday evening, one official said.
Rescue boats brought some survivors to Safaga, where the ferry was meant to arrive on Friday morning, one security official said.
But Egyptian aircraft also saw bodies floating in the water, security sources said.
Most of the passengers were Egyptians working in Saudi Arabia, officials said, but at this time of year many Egyptians are still on their way home from the annual pilgrimage to Mecca.
The Egyptian state news agency MENA quoted official sources in Safaga as saying the ferry had sunk 57 miles from the Egyptian port of Hurghada, north of Safaga.
"Some of the passengers survived," it added.
The ferry was on an overnight trip between the Saudi port of Duba and Safaga, both at the northern end of the Red Sea. It had originally come from Jeddah, the main port for the pilgrimage.
Coastal stations did not receive any SOS message from the crew, said Adel Shukri, the head of administration at el-Salam Maritime Transport Company, which owns the ferry.
Another company official, Andrea Odone, said he could not confirm that the ship had sunk or that there were any survivors. "It could take some hours to work out what happened," Odone told Reuters from the company headquarters in Cairo.
Transport Minister Mohamed Lutfi Mansour told MENA the armed forced had deployed four rescue vessels at the scene.
A Saudi border control official in Jeddah said: "We don't know yet what happened -- if it sank, or overturned, or what."
According to the company's Web site, the Al Salam 89 can carry about 1,400 passengers. Egyptian officials and media called it the Al Salam 98 but the company's Web site names it as the Al Salam 89.
A sister ship, the Al Salam 95, sank in the Red Sea in October after a collision with a Cypriot commercial vessel. In that case almost all of the passengers were rescued.