The privately owned ferry left Kyrenia port at 12:30pm local time and immediately started taking on water for an unknown reason, authorities said. It was heading for the Turkish port of Tasucu in the eastern Mediterranean.
Survivors reported the ferry moving erratically, with its last hard impact with the water's surface breaking the bow of the two-hulled vessel, allowing water to seep in.
Turkish Cypriot authorities arrested the captain and the other seven crew members, EFE reported.
The disaster occurred just off the coast of Kyrenia, a popular holiday resort for both locals and tourists.
The ferry was one of several shuttle sea services that link north Cyprus, a breakaway, unrecognised Turkish Cypriot state, with Turkey daily.
Turkish Cypriot leader Tufan Erhurman told CNN Turk he was "deeply saddened" by the incident.
Video footage showed people in red life jackets sitting or standing on top of the overturned vessel as authorities scrambled coastguard and private vessels to bring them to shore.
"The vessel had been moving very badly. It was constantly lifting out of the water and slamming back down. It was shaking violently," survivor Efe Multici told CNN Turk.
"Three or four minutes later, the ferry leapt high into the air, then came crashing down. The front left side burst open and water started pouring in."
By late afternoon, the ship had sunk, settling on the seabed at a depth of 514 metres. Divers from Turkey would be assisting the search, they said.
"If there are people still inside the vessel, reaching them does not appear easy at the moment," Erhurman said.
"Efforts are being made using other technologies to reach them as well."
Cyprus was battered by fierce storms on Saturday, with one person dying after his sailboat crashed onto rocks in rough seas in the island's south-east.
Asked about the cause of the tragedy, Erhurman noted the storm on Saturday, but said the weather on Sunday was considered suitable for travel.
"There is a great sense of shock here. This is not something we have experienced before," he said, speaking from the crisis centre set up in the area.
North Cyprus is a breakaway state recognised only by Turkey, which supports the area economically and militarily.
In Turkey, President Tayyip Erdogan extended his condolences to the families affected.
"Efforts to reach those who are still missing continue uninterrupted," Erdogan said.
"God willing, we hope to receive positive news from these efforts."
Expressions of condolence and offers of assistance also came from Cyprus's internationally recognised government.
Cyprus has been split along Greek and Turkish Cypriot lines since 1974, when Turkey invaded in response to a brief Greek-inspired coup.
