The bus was traveling 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, security officials said.
The exact number of injured was not immediately known, but Egyptian officials told the Associated Press at least 17 people were hurt.
Most of the injured included tourists, including South African nationals, security sources told Reuters.
The officials said security forces cordoned off the site of the explosion and the wounded were taken to a nearby hospital.
Pictures posted to social media showed a bus with its windows cracked and debris in the road as some people tended to their injuries.
A witness to the blast, Mohamed el-Mandouh, told Reuters he heard a "very loud explosion" while sitting in traffic near the area. Egyptian officials told the AP that security forces cordoned off the site of the explosion and the wounded were taken to a nearby hospital.
Atif Moftah, the 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, which 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.
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.
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.
The Associated Press contributed to this report.