Bouteflika wasadmitted to the cardiology unit of the Alembert clinic in Grenoble after being flown to France on Thursday, according to the Dauphiné Libéré newspaper, which says that the entire floor has been booked for security reasons.
Over 30 French riot police were deployed around the hospital and the street has been cordoned off.
A convoy including an ambulance carrying the Algerian president left the clinic, heading for the airport, on Saturday afternoon.
Although Algerian officials have not confirmed the news and the exact reason for his hospitalisation has not been mad epublic, a French government source has and French police say Bouteflika flew into Grenoble on Thursday.
The head of cardiology at the Alembert used to work at Paris’s Val de Grâce hospital, where Bouteflika spent 80 days being treated after suffering a “minor stroke” in 2013.
He returned to Paris for minor treatment in January.
Bouteflika has been Algeria’s president since 1999 and has not openly indicated a preference for his successor, leading to widespread speculation as to both his state of health and who could replace him.
After returning to Algiers in a wheelchair last July, he was not seen in public for months and his appearances since then have been rare, although he has been seen more often on TV.
On Monday he met French Foreign Affairs Minister Laurent Fabius and Economy Minister Emmanuel Macron, who were in Algeria for the opening of a Renault car factory.
Although a diplomat who met him recently described him as “lucid”, his residence has been completely adapted to allow him to move around it in his wheelchair.
Boutelfika was elected president for the fourth time, with more than 80 per cent of the vote, in April.