The stranded are thought to be Syrian refugees.
The refugees were taken aboard the Salamis Filoxenia, Limassol port master Girgos Pouros said. All are said to be in good health.
Most of the people on the small fishing boat that sent a distress signal were women and children.
They were spotted 55 nautical miles south of the town of Paphos.
“It was quite a difficult operation,” Kikis Vasiliou, director of Salamis Cruises that owns the cruise ship, was quoted as saying by the Cyprus Mail website.
“All the passengers are safe.”
The vessel was expected to dock in Limassol later on Thursday, September 25.
Cypriot authorities earlier said they picked up a radio distress signal as the boat was caught in rough seas.
This year has seen a dramatic increase in the number of migrants crossing the Mediterranean in overcrowded boats – particularly people fleeing the conflict in Syria. The majority have headed for Italy and Malta.
Libya, racked by unrest and lawlessness, has become a major people-trafficking hub. However, Cyprus lies closer to Syria.
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