Nekkaz, who sought to run against Bouteflika in Algeria's upcoming elections, said he had come to the University Hospitals of Geneva (HUG) to seek information about the ailing 82-year-old leader.
He staged a demonstration with several dozen supporters outside HUG and then announced he was going inside. He was arrested for trespassing following a complaint by the hospital, and was also accused of resisting arrest, police spokesman Jean-Philippe Brandt told AFP, adding that Nekkaz was set to be presented to a prosecutor on Saturday.
Bouteflika, in power since 1999, has rarely been seen in public since suffering a stroke in 2013. His bid to secure another term at Algeria's April 18 election has sparked waves of protests, dominated by youths who have called for the defiant president to stand aside.
On Friday, tens of thousands protested across the country, chanting “No fifth term — hey, Bouteflika!” and waved Algeria's green-white-and-red flags.
“There are 40 million Algerians who want to know where the president is,” Nekkaz told the crowd of a few dozen people that had assembled outside HUG.
Bouteflika has been in Switzerland for nearly two weeks receiving what his office has called routine medical checkups. Algeria has not officially confirmed that Bouteflika is at HUG, but multiple Swiss media reports have placed him at the hospital.
An AFP journalist also heard hospital staff discussing Bouteflika's presence on HUG's eighth floor, where the VIP wing is located, and there was a large deployment of police outside the hospital on Friday.
Nekkaz — an increasingly popular activist with a large social media following — suggested that Bouteflika was actually dead.
“The entire world, and all of Algeria knows that he is no longer of this world,” he told reporters, charging that powerful players in Algeria had an interest in maintaining the illusion that Bouteflika was alive to keep their grip on power in the country.
Bouteflika's campaign manager Abdelghani Zaalane meanwhile insisted Thursday that the president's health raised “no worries”. The medical examinations Bouteflika had been undergoing in Switzerland were nearly completed, he said.
Nekkaz was himself earlier this week denied the right to stand in the vote, apparently falling foul of a law which bans candidates who have ever possessed a nationality other than Algerian. This despite the fact that he had renounced his French citizenship and also gathered the necessary 60,000 voter signatures needed to run.
But Nekkaz instead put forward the candidacy of his cousin and namesake, an Algerian mechanic, with the explicit intention of using inventive measures to take over the presidency if his relative is elected.
Algeria's constitutional committee is due to determine on March 13 if the presented candidacies are legitimate. Nekkaz urged the committee not to accept the candidacy of Bouteflika.
“It is impossible to continue to support an election with a candidate who is in fact dead,” he said.
By AFP's Agnès Pedrero