He was released on bail after accepting central government control over the region but still faces the prospect of a trial.
A judge said the five were serious flight risks.
Speaker Roger Torrent announced to the chamber on Saturday that there would be no vote on the candidacy of Jordi Turull, a former regional minister.
One protester there, Carme Sala, said: "There are two million people who want to leave Spain and they can't put us all in prison."Catalan TV showed rallies in support of the jailed leaders elsewhere in the region including in the cities of Vic and Tarragona".
Altogether 25 separatists have been charged variously with sedition, rebellion, embezzlement and other crimes.
Mr Puigdemont and fellow separatists have all denied any wrongdoing, saying the plebiscite gave them the authority to break away from Spain.
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Who are the latest to be detained?
All five spent some time in detention following the banned referendum but were released on bail late previous year pending investigations into their individual roles in the vote.
He and other secessionist leaders are due to appear before the Supreme Court on Friday morning for the opening of a new phase in the investigation which precedes a trial.
Five other Catalan politicians, including Mr Puigdemont, fled to Brussels following the failed secession attempt in late October.
Llarena also issued worldwide arrest warrants for former Catalan President Carles Puigdemont, who is in self-imposed exile in Belgium along with four of his former ministers.
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What else did the judge say?
But one of them, Marta Rovira, ignored the summons and instead announced she was taking "the road to exile".Rovira is deputy leader of the leftwing separatist ERC party, whose chief is now in jail. Leaving the country was "the only way I have to stand up against the government of the Partido Popular", she wrote, referring to the conservative party of Spanish Prime Minister Mariano Rajoy.
A Spanish supreme court judge has charged Jordi Turull, Catalonia's presidential candidate, with rebellion and ordered him to remain in custody less than 24 hours before he was due to attend an investiture debate.
What reaction has there been?The court could rule the candidate ineligible to hold office or imprison him if it finds there is enough incriminating evidence, thus torpedoing any hopes of a second debate later today.
Occasional clashes broke out between riot police and protesters as the large crowds pushed against police cordons, La Vanguardia reports.
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