Since Egypt's military ousted Islamist president Mohamed Morsi in 2013, the authorities have accused Hamas, which controls the Gaza Strip, of aiding jihadists who have increased their attacks on security forces in the Sinai Peninsula.
Today's court verdict followed a complaint from a lawyer accusing the Hamas armed wing of direct involvement in "terrorist operations" in the Sinai, a court official said.
The lawyer also accused the movement of using tunnels under the border between Egypt and Gaza to smuggle arms used in attacks against the police and army, the official said.
In early January, Egypt began work on doubling the width of a buffer zone along the border with Gaza to prevent militants infiltrating from the enclave.
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The buffer zone was created following a suicide bombing on October 24 last year that killed 30 Egyptian soldiers and wounded scores.
After that incident, Cairo declared a three-month emergency in parts of North Sinai, a remote but strategic region bordering Israel and Gaza.
In the latest incident in the region, an Egyptian interior ministry employee was killed a day after jihadists aligned with the Islamic State (IS) group killed 30 people in the peninsula.
On Thursday, militants from Ansar Beit al-Maqdis -- which has pledged allegiance to IS in Iraq and Syria -- claimed a string of attacks, including a car bombing, that left at least 30 people dead.
Jihadists in the Sinai have killed scores of policemen and soldiers since Morsi's overthrow, vowing revenge against a crackdown on his supporters that has killed more than 1,400 people.
Last March, Cairo banned and outlawed Hamas operations on Egyptian soil, ordering the freezing of its assets.