The men were arrested yesterday in the Nile Delta province of Sharkiya on suspicion of crimes including "promoting the ideology of the Muslim Brotherhood group, distributing its leaflets, and inciting violence against the army and police".
The government declared the Brotherhood a terrorist organisation on Christmas Day, accusing it of carrying out a suicide attack that killed 16 people the previous day. The Brotherhood condemned the attack.
Earlier yesterday, a bomb blast hit a bus in Cairo's Nasr City district, injuring four people.
The homemade device had been put on a traffic island and a second one, found nearby, was dismantled,
Attacks across Egypt over the last few days have raised fears of intensifying violence in the run-up to a constitutional referendum in January as the interim government pushes ahead with an army-backed plan for political transition.
The government has vowed to fight "black terrorism" after Tuesday's deadly attack on a police compound in the city of Mansoura which also injured about 140 people.
Bomb attacks and shootings have become an almost daily occurrence in the Sinai peninsula since the army toppled Islamist President Mohamed Mursi in July following mass protests against his rule.
The unprecedented decision to declare the Brotherhood a terrorist organisation is likely to end any chance of reconciliation between the government and the 85-year-old Brotherhood which is still Egypt's most organised political group.
It marks a stunning reversal of fortunes for the long-outlawed organisation that saw member Mr Mursi reach Egypt's highest office in the country's first democratic election, only to be ousted in a popularly-backed military coup in July.