Swiss police said Rachid Nekkaz - a businessman and political activist opposed to Bouteflika - was arrested on Friday outside the Geneva hospital where the president is being treated.
Algeria has more than 1.7 million students, of whom almost 630,000 are housed on campuses.
Earlier, Nekkaz said he had come to the hospital seeking answers about the condition of Bouteflika, whose bid to secure another term at the April 18 election has sparked protests.
On Friday, tens of thousands of protesters took to the streets of Algerian cities in the biggest demonstrations yet against his rule.
In the latest demonstration, hundreds of lawyers in black robes rallied in downtown Algiers on March 8 as momentum gathered in the country's most sustained protests since the 2011 Arab Spring.
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Algerian police have denied reports about fatalities among security forces during Friday's protests against a re-election bid by incumbent President Abdelaziz Bouteflika.
He could also not have himself issued a statement this week that warned protesters in Algeria that troublemakers may try to infiltrate the demonstrations and create "chaos", according to the petition.
Riot police fired tear gas to prevent the mostly peaceful groups from reaching a road leading to the presidential palace, and local reports said almost 200 people were detained by the security forces.
The president, who is confined to a wheelchair, has rarely been seen in public since suffering a stroke in 2013, prompting critics to question whether he is being used as a puppet candidate by a faction of civilian and military figures. One scenario, he says, "is that the president steps down, handing power to the head of parliament".
He has been in Switzerland for almost two weeks receiving what his office has called routine medical checkups. Other commitments are aimed at developing and adopting a new Constitution through a referendum for the birth of a New Republic and the new Algerian system.