One man quoted bystanders as saying four cars had exploded in the car park of an upmarket hotel in the area.
The first explosion, shortly after one a.m. (2200 GMT), was audible more than one km (half a mile) away, one resident said. It started a fire and smoke billowed over the town.
About 15 minutes later, two explosions were audible from the direction of Naama Bay, about six km away, he said. Naama Bay has dozens of luxury hotels popular with divers and holidaymakers from Europe.
Another resident said one of the explosions came from the direction of the Moevenpick Hotel in Naama Bay and broke the windows of his apartment. It was unclear how far away he was from the blasts.
A third person, Ahmed Fawzi, an Egyptian lawyer visiting Naama Bay on business, told Reuters that one of the explosions ripped the door of his office off its hinges.
When he went outside to find out what happened, bystanders said four cars had exploded in the car park of the Moevenpick Hotel. President Hosni Mubarak has a holiday villa in the adjacent Golf Hotel.
Three tourists were killed and others injured in two bombings in the Egyptian capital Cairo in April.
Egypt's tourism industry, based on Red Sea resorts like Sharm el-Sheikh and on its pharaonic ruins, proved resilient after earlier bombings in the Sinai peninsula in October, which killed 34. Those attacks were seen as targeting mainly Israelis.