The officials said the bus was travelling on a road close to the under-construction Grand Egyptian Museum, which is located adjacent to the Giza Pyramids but is not yet open to tourists.
The bus was carrying at least 25 people mostly from South Africa, officials added.
The attack comes as Egypt's vital tourism industry is showing signs of recovery after years in the doldrums because of the political turmoil and violence that followed a 2011 uprising that toppled former leader Hosni Mubarak.
The officials said security forces cordoned off the site of the explosion and the wounded were taken to a nearby hospital.
The explosion damaged a windshield of another car, they said. Footage circulated online shows shattered windows of the bus.
The officials spoke on condition of anonymity because they were not authorised to brief media.
Atif Moftah, general supervisor of the Grand Egyptian Museum, said the explosion did not cause any damage to the museum, in a statement issued by the antiquities ministry.
No group has immediately claimed responsibility for the attack. It is the second to target foreign tourists near the famed pyramids in less than six months.
In December, a bus carrying 15 Vietnamese tourists was hit by a roadside bomb, killing at least three of them.
Egypt has battled Islamic militants for years in the Sinai Peninsula in an insurgency that has occasionally spilled over to the mainland, hitting minority Christians or tourists. The insurgency gained strength after the 2013 military overthrow of the country's first freely elected president, an Islamist whose brief rule sparked mass protests.
(story provided by news agency PTI)