At least 17 people have been injured near the new Egyptian museum, according to officials.
Most of the injured were foreign tourists and some of these were from South Africa.
There were at least 25 people on the bus.
Images shared on social media showed windows of a bus had been smashed and tourists fleeing the vehicle.
Some appeared to be injured and bloodied from the incident.
A witness, Mohamed el-Mandouh, told Reuters he heard a "very loud explosion" while sitting in traffic close to the blast.
Images also showed an ambulance at the scene and debris in the road next to a low wall with a hole in it.
Security forces cordoned off the site of the explosion and the wounded were taken to a nearby hospital.
In a statement issued by the antiquities ministry, Atif Moftah, general supervisor of the Grand Egyptian Museum, said the explosion did not cause damage to the museum.
The area is a popular tourist destination and the pyramid of Giza is the oldest of the seven wonders of the world.
The pyramids are in Giza City, which is around eight miles away from the centre of Cairo.
It is the second attack to target foreign tourists near the famed pyramids in less than six months. No group has immediately claimed responsibility for the latest attack.
In December, three Vietnamese tourists and an Egyptian guide were killed and at least 10 others injured when a roadside bomb hit their tour bus less than two-and-a-half miles from the Giza pyramids.