Bouteflika, 76, was flown to the Val de Grace hospital in Paris three weeks ago following a mini-stroke and speculation has been rife about the state of his health.
In a statement, the French defence ministry confirmed that the Algerian leader had been hospitalised at his request at Val de Grace on April 27.
“Mr Bouteflika is today leaving Val de Grace for another facility in order to continue his convalescence,” the statement said, without providing further details.
Algerian authorities broke official silence on Bouteflika’s health on Monday, confirming he was recovering in Paris after a mini-stroke and saying his life was “never in danger”.
The secrecy surrounding his treatment in France led many in Algeria to speculate about the health of the president, who has ruled Algeria since 1999.
Authorities have denounced “false information” about his health and insisted Bouteflika has been keeping track of government activities.