Published: 2018-12-29 17:11:29 BdST
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.
Security forces also killed 10 suspected militants in North Sinai, where the country is fighting an insurgency led by Islamic State.
State news agency MENA said that the suspects were killed in a gun battle.
The ministry did not give any details about the suspects' identity or whether there had been any casualties or injuries among the security forces. The statement said the three raids took place simultaneously.
The ministry published photos of bloodied bodies with their faces concealed and assault rifles and shotguns lying on the floor beside them.
Three Vietnamese tourists and an Egyptian guide were killed and at least 10 others injured when a roadside bomb blast hit their tour bus on Friday less than 4 km from Egypt's world-famous Giza pyramids.
Egypt's military and police launched a major campaign against militant groups in February, targeting the Sinai Peninsula as well as southern areas and the border with Libya.
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.