The bombing took place in the Haram district, Giza Region where the world-famous Giza Pyramids are located. Egypt's prime minister said the bus had taken a different route to the one which was secured by forces.
There was no immediate claim of responsibility for the attack.
The bus was traveling in the Marioutiyah area near the pyramids on Friday (local time) when the crude roadside bomb, concealed by a wall, went off. At least 10 Vietnamese tourists and the Egyptian bus driver were wounded, authorities said.
The interior ministry confirmed the death of two of the tourists, and the state prosecutor's office later said a third had died.More news: India 346-4 at tea in 3rd test against Australia
Saigon Tourist, the tour company that organised the trip, said the Vietnamese tourists were "on their way to a restaurant for dinner" when the bomb exploded.
Islamist extremists, including militants linked to Islamic State, are active in Egypt and have targeted foreign visitors in the past.
The ministry did not say whether the suspected militants were connected to Friday's attack, but said its forces killed 30 people during raids on their hideouts in Giza where it said "terrorist elements" were planning a series of attacks targeting state institutions and the tourism industry.
Egypt has for years been battling an armed movement in the thinly populated Sinai, which has gained pace since the military overthrew democratically elected President Mohamed Morsi of the Muslim Brotherhood in mid-2013.
That incident dealt a severe blow to Egypt's tourism industry still reeling from the turmoil set off by the 2011 uprising that forced veteran leader Hosni Mubarak from power.