The interior ministry said in a statement on Wednesday that the organisation, calling itself the Victorious Group, had members in suburbs northeast and south of the capital.
"Information, documents and interviews ... confirmed that they were studying carrying out terrorist operations against tourist targets, the gas pipeline on the Greater Cairo ring road and some sensitive sites through bombings," it said.
"They were also studying targeting some Muslim and Christian religious figures and ... what they called degenerate youth in tourist areas," it said.
The statement listed 22 members led by Ahmed Mohamed Ali Gabr, 26, a humanities student. It did not say how many had been arrested.
It said they had downloaded information from the internet on how to make explosives and poisons. It did not mention any weapons.
But a spokesman for the opposition Muslim Brotherhood said the interior ministry announcement was predictable.
"The government is going to announce such operations to justify the extension of the state of emergency," Hamdi Hassan said.
Emergency laws have been in force almost continuously since 1967 and their abolition has topped the list of priorities of most of the country's opposition movements.
The ministry said: "[They had] deviant extremist ideas far from true Islam and a mistaken and perverse response to international and regional events."
The group is alleged to have been trying to buy land in El Saff, about 60km south of Cairo, for a training base, and had been in contact with groups abroad to get help in sending members abroad to fight, it said.
"Information, documents and interviews ... confirmed that they were studying carrying out terrorist operations against tourist targets, the gas pipeline on the Greater Cairo ring road and some sensitive sites through bombings"
Egyptian interior ministry
An Islamist group planted two bombs in Cairo in April 2005, killing four people and wounding many others. The bombings appeared to be aimed at tourists.
A separate group attacked the Red Sea resort of Sharm al-Shaikh in July, killing at least 67 people. Some information from the government suggested that the Red Sea bombers also had militant views.
Also on Wednesday, Egypt's prosecutor-general, Maher Abdel Wahed, ordered the release of 120 university students suspected of being members of the outlawed Muslim Brotherhood.
Most of the group had been rounded up in several provinces in the past two weeks for joining a banned group, a police official and group members said.