Egypt’s interior ministry said the bus was travelling from St Catherine’s Monastery, a popular tourist destination in the south of the peninsula near the border with Israel, when it was attacked.
State television showed a photograph of the bus with the windows blown out and the roof partially torn off. Plumes of black smoke billowed from the site of the explosion on a palm tree-lined boulevard.
Security sources said an explosive device planted either inside or near the bus was used.
Islamist militants based in the largely lawless Sinai have stepped up attacks on government security forces since army chief Abdel Fattah al-Sisi ousted Egypt’s elected president, Mohammed Morsi of the Muslim Brotherhood, in July.
If militants were behind the latest attack, it would mark a shift in strategy to targeting tourists and economic targets rather than just Egyptian police and soldiers.
Morsi on trial
Mr Morsi and 35 other members of the Muslim Brotherhood appeared in court on Sunday to face charges of espionage.
They are accused of conspiring with the Palestinian militant group Hamas, Lebanon’s Hezbollah and others to carry out a campaign of violence to destabilise Egypt following the president’s overthrow.
The charges are the most serious accusations yet in a series of trials against the Muslim Brotherhood and potentially carry the death penalty.
The espionage charges link the group to the Islamic militant insurgency in Sinai and claim that the Brotherhood has been working with extremists since 2005 in deals aimed at attaining and holding onto power.