A ministry statement linked the militants to Hasm, an armed affiliate of the Muslim Brotherhood, and said authorities found explosives, weapons and ammunitions at two different raid sites.
The operation came a day after a roadside bomb hit a tourist bus near Egypt’s Giza pyramids. That blast wounded 17 people.
There was no claim of responsibility for the bomb attack, and the interior ministry did not link Monday’s raids to the blast.
Officials said the bus was carrying 28 people, most of them South African tourists. Videos circulating online show the bus windows blown out or shattered.
South African Ambassador Vusi Mavimbela and his team in Egypt are visiting victims in hospitals, officials said.
The explosion took place near the Grand Egyptian Museum, which is under construction near the Giza pyramids. A statement issued by the antiquities ministry said the explosion caused no damage to the museum.
In December, three Vietnamese tourists and one Egyptian guide were killed when a bomb hit their bus near the Giza pyramids.