Two Australian women are among those injured, and an Australian foreign affairs official is being sent to Dahab to help them and any other Australians affected.
Witnesses in the small beach and diving resort, which is popular with backpackers, described scenes of carnage and chaos.
A cafe worker who was about 200 metres from the scene said “We saw many dead people. People were screaming. People were being taken to hospital. Egyptians went to give blood. There were body parts. There’s police everywhere.”
“There were body parts and debris in the street … There are ambulances and cars taking people to hospital,” said another resident.
The explosions, which came at the height of the tourist season, took place at the Nelson Restaurant, the Aladdin Cafeteria and the Ghazala Supermarket, the Interior Ministry said.
An official with the local ambulance service said many of the dead appeared to be foreigners.
The resort of Dahab, is popular with western backpackers, budget Israeli tourists and was also packed with Egyptians enjoying a public holiday. It is renowned for its diving, snorkelling and windsurfing.
The bomb blasts struck on Sham el-Nessim, a traditional holiday which marks the beginning of spring, and a day before Sinai Liberation Day, which celebrates Israel’s withdrawal from the peninsula in 1982.
The streets of Dahab were immediately sealed off by police and Egyptian security sources said the border with Israel, which lies only around 100 miles north of Dahab, was closed to prevent the attackers from fleeing.
State television said the blasts appeared to have been the result of remote-controlled bombs, not suicide bombers.
Egyptian President Hosni Mubarak pledged that the perpetrators of the attacks would be punished, while US President George W. Bush condemned the bombings as a “heinous act”.
Israeli Defence Minister Shaul Mofaz offered to send army rescue teams and doctors, while hundreds of Israeli tourists were rushing home after the blasts.
A state of alert was declared at the main hospital in the Israeli border town of Eilat to handle any casualties sent for treatment and to free up doctors to dispatch to the scene.
Approximately 20,000 Israeli holidaymakers were believed to have been in the Sinai at the time of the blasts despite repeated warnings from their government of the risks of attack by Islamic militants.
But public radio quoted Israeli ambassador in Cairo Shalom Cohen as saying he had been informed there were no immediate reports of Israeli casualties.
The resorts of Egypt’s south Sinai Peninsula have been repeatedly hit by Islamic militants in recent years.
Multiple bombings in the Red Sea resort of Sharm el-Sheikh at the tip of the Sinai killed some 70 people in July 2005, the deadliest to have hit Egypt since a major wave of Islamist terrorist attacks in the mid-1990s.