The museum, still under construction, is set to be the largest archaeological museum in the world when it opens in 2020.
Seventeen people, including foreigners, were injured, security and medical sources said.
Images show bloodied tourists leaving the bus, with ambulance crews on the scene.
Initial reports from state media indicate 10 Egyptians and seven South Africans were among those injured.
An official at the nearby Al-Haram Hospital told CNN that they received the tourists who were wounded in the blast.
There are no reports of deaths in the blast so far.
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A witness, Mohamed El Mandouh, told reporters that he heard a "very loud explosion" while sitting in traffic near the site of the blast.
The Hasm group emerged in 2016 and has in the past claimed responsibility for several attacks.
Cairo has been battling Islamic insurgents on the Senai Peninsula for years.
While Sunday's attack near the Pyramids caused no fatalities, it is likely to affect Egypt's vital tourism sector, which has been making a marked recovery after years of turmoil following a 2011 uprising.
It is the second to target foreign tourists near the famed pyramids in less than six months.
The attack comes almost five months after three Vietnamese tourists and their Egyptian tour guide were killed when a bomb hit their tourist bus as it was travelling on El-Maryoutiya Street in Giza's Haram district.