The bus was carrying a total of 14 Vietnamese tourists, it added, saying only two of them escaped unharmed.
According to officials, the explosion occurred at 6:15PM local time when the bus passed a section of wall used to hide the device from motorists and pedestrians.
The bombing took place in the Giza region near Cairo, where the pyramids are located.
Police are investigating, the statement said.
An interior ministry statement said ten other tourists from Vietnam as well as the Egyptian bus driver were wounded when the homemade device exploded in the early evening.
The PM said that the number of injured still under treatment stands at 10 with two in critical condition.
He also ordered prosecutors to conduct a forensic investigation of the materials used to make the IED and to collect all surveillance camera footage in the vicinity of the explosion, the news outlet reported.
Mr Madbouli said that the Egyptian tour guide had died in hospital from his wounds.
The government says fighting Islamist militants is a priority as it works to restore stability after the years of turmoil that followed the "Arab Spring" protests of 2011.
Egypt's foreign ministry spokesman Ahmed Hafez called Friday's attack a "cowardly" terrorist act targeting the willpower of the Egyptian people.