The tourist bus crashed through a guard rail and down the ravine after it tried to overtake another tour vehicle in a no-pass area, Rami Azani, the driver of the second bus, said.
Among those wounded, 15 were in a critical condition, according to rescue services.
"It may well be that this could be the worst bus accident in Israel's history; it is certain ly the worst in the last 20 years," Dan Nolan, Al Jazeera's correspondent in Jerusalem, said.
"Wreckage has been strewn across a wide area. Rescuers not only have to try to free those trapped inside the bus but treat others thrown from the bus as it rolled down the hill.
"Even the Israeli health ministry has called for any doctors or nurses who are on holiday in Eilat to actually come down to the local hospital to help out."