The six French passport holders, five men of Turkish descent and one of Algerian origin, were detained on Saturday evening after arriving at Larnaca airport on a flight from Basel, Switzerland, police said.
They will then be handed back to French authorities.
Police said the suspects were aged between 25 and 33.
Justice Minister Ionas Nicolaou told state radio that at least three of the six appeared to have “strong links to terrorist groups”.
“There were suspicions against these specific individuals upon their arrival at the island,” Nicolaou said.
“We have information suggesting that they have strong links to terrorist groups, while Interpol has already informed us that three of those suspects have been identified as having links to a terrorist organisation,” he said.
“The other three also appear to have some sort of link,” he said.
Nicolaou later told reporters that “these people… will be sent back for reasons of security”.
There was no indication they had planned to stay in Cyprus but were more likely in transit, he said, without specifying if they were headed for Syria.
Once they return to Switzerland — Larnaca has a scheduled flight to Basel on Tuesdays — the suspects will be handed over to French authorities, Swiss federal police told AFP.
“This has been discussed with French authorities, they are the ones in charge of the case and they will take care of the suspects once they arrive,” a spokesman said.
A French source close to the case said there was “no suggestion at this stage of any suspicions of terrorism against them”.
The six travellers were known to the French authorities as part of a Muslim association, the source said.
“This is a group of bearded men who openly have an Islamic appearance,” the source said, adding that like all other passengers on the flight to Larnaca, they had been checked by the French authorities.
Cyprus has stepped up security at its airports, ports and other public places following the jihadist attacks in Paris earlier this month that left 130 people dead.