The explosions occurred in a bustling area popular with tourists during the early evening when many people would have been out in cafes and restaurants.
Eyewitnesses spoke of seeing debris and body parts in the streets.
Southern Sinai peninsula resorts have been hit before. About 60 people were killed in Sharm el-Sheikh last July.
Most of the dead were Egyptians, who had been enjoying a Spring holiday in Dahab when the attacks occurred. A German boy was among three foreigners killed.
Some officials were quoted as saying the attacks were the work of suicide bombers, but others said it was too early to say. There has been no immediate claim of responsibility.
There were lots of bodies around, people running with blood coming out of their faces
Australian tourist Owen Norris
Witnesses tell of horror In pictures: Dahab blasts UK condemns attacks
The attacks received swift international condemnation.
Egyptian President Hosni Mubarak called the explosions a "wicked terrorist act", and US President George W Bush described it as "heinous".
The Hamas-led Palestinian government said it "strongly condemns this criminal act which flouts our religion, shakes Palestinian national security and works against Arab interests".
Israel's ambassador in Cairo urged Israelis in Sinai to leave immediately, and a stream of Israeli cars were reportedly heading to the Israeli border at Taba by late evening.
'Like war'
The three explosions happened in quick succession at about 1900 (1700GMT) in what is a small, low-key resort popular with Western backpackers, budget Israeli tourists and scuba-divers.
Several restaurants, shops and a supermarket were destroyed in the main tourist street close to the seafront during one of the busiest times of the day.
ATTACKS ON EGYPT TOURISM July 2005: Bombings in Sharm El-Sheikh kill 64, mostly tourists April 2005: Two attacks on tourists in Cairo, leave three dead October 2004: Bombings in Taba and Ras Shitan kill 34, including 12 Israelis Nov 1997: Gunmen kill 58 tourists and three policemen at Hatshepsut temple in Luxor Sept 1997: Nine German tourists killed in a bomb attack at Egyptian museum in Cairo April 1996: Gunman kills 19 Greek tourists outside Cairo hotel
World reaction Militants target tourists
A German doctor, who was holidaying in the town at the time, said a 10-year-old boy died in his arms as he went to the aid of the wounded.
"It was like war," Michael Hartlich told the AFP news agency, still shocked and upset several hours after the blasts. "I'd never seen anything like it before, a child, a baby, blood everywhere, the smell of burnt skin, of burnt hair."
The BBC's Mark Perrow in Dahab saw people sitting dazed near to where the explosions took place as police set up cordons.
The roads in and out of Dahab were being controlled by checkpoints and a virtual curfew existed overnight in the town, our correspondent says.
The emergency services were quickly on the scene, and many volunteers rushed to the town's small hospital to give blood.
The worst of the injured were driven 80 kilometres (50 miles) for treatment at Sharm el-Sheikh or flown on to the capital, Cairo.
Among the 62 wounded there were three Danes, three Britons, two Italians, two Germans, two French people, a South Korean, a Lebanese, a Palestinian, an American, an Israeli and an Australian.
Militant group
Dahab, which means gold in Arabic, lies on the coast of the Gulf of Aqaba, about 100 kilometres (65 miles) south of the border with Israel.
In July 2005, more than 60 people died in a bomb attack in the tourist area of the resort town of Sharm al-Sheikh, further south along the coast.
The BBC's Heba Saleh says the Egyptian authorities have uncovered a militant group active in the Sinai, but they have said very little about it.
The group is also thought to have been responsible for bombings in the resort of Taba in October 2004, when 34 people were killed.
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Egypt
Three explosions rocked the Egyptian resort city of Dahab and killed at least 24 people. Between 60 and 150 people were injured in the attack.

The blasts came at the height of the tourist season, officials said. The three time bombs exploded in a busy restaurant and in a market area in the Red Sea resort city within a span of five minutes.

Dahab is located on the Gulf of Aqaba on the eastern side of the Sinai Peninsula.