"We received information about one individual... That he might commit violent acts in France," Cazeneuve said on French television.
"So this morning he was arrested along with three members of his entourage and checks are under way. I call on everyone to be extremely prudent regarding reports that are circulating about an imminent violent act."
Police sources said earlier that three men and a woman were arrested in the dawn raid who were not thought to be planning an imminent attack but were "of interest".
The four had been under surveillance by French intelligence on suspicion of a "possible plan to attack" but the threat has not been confirmed, the sources said.
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Police raids have turned up no weapons, but computer hardware and data have been seized for analysisd, they said.
"You can't at this stage talk about a plan of imminent attack," one police source said.
The arrests were carried out at dawn in two Paris districts and the rundown northern suburb of Saint Denis, the scene of a massive raid after the November 13 attacks during which the suspected ringleader, Abelhamid Abaaoud, was killed.