South African tourists are among the injured. Most of those hurt suffered minor injuries, while three were treated in hospital, officials say.
A device went off close to the museum fence as the bus was passing.
It is not yet known who was behind the bombing but Islamist militants have attacked tourists in Egypt in the past.
In December, three Vietnamese tourists and a local tour guide were killed after a roadside bomb hit their bus.
A witness, Mohamed el-Mandouh, told Reuters news agency he had heard a "very loud explosion" while sitting in traffic near the site of the blast, which is close to the capital Cairo.
The blast hit the bus which was carrying 28 passengers, Egyptian Tourism Minister Rania A Al Mashat said.
Images taken after police cordoned the bus show a vehicle with windows blown out or shattered, and glass littering the aisle inside.
A private car was also damaged behind the bus.