They were found guilty of organizing a recent unauthorized protest.
Ahmed Maher, Ahmed Douma and Mohamed Adel were arrested after protesting in November over a new controversial law that restricts demonstrations.
The three well-known activists have long called for greater democracy in Egypt.
Ahmed Maher and Mohamed Adel were founding members of the April 6th Youth Movement, which led protests to remove long-time President Hosni Mubarak in 2011.
The three were among a group of demonstrators outside the upper house of parliament in late November protesting over the new law, which states that public gatherings of more than 10 people must be authorized.
The military-installed government has defended the law, saying it is not intended to limit the right to demonstrate but rather to “protect the rights of protesters”.
But its opponents say the law has in effect replaced a recently expired state of emergency, and is stricter than the measures in place during the rule of Hosni Mubarak.
The men are the first to be jailed under the new law. The court in Cairo found them guilty of holding a demonstration without authorization and attacking police officers.
State-run television said the men had been sentenced to three years’ hard labor. They have also been ordered to pay a $7,000 fine each.
As the verdict was read out, the courtroom erupted with chants of “Down, down with military rule! We are in a state, not in a military camp”, Reuters news agency reports.
Until recently, the main targets for arrests by the authorities had been Islamists, many of whom continue to protest over the ousting by the military of the Muslim Brotherhood-backed government of Mohamed Morsi in the summer after weeks of mass protests.
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