President Bouteflika's candidacy had provoked mass protests across Algeria over the past few weeks.
He has led Algeria for 20 years but has been rarely seen in public since he suffered a stroke in 2013.
No new date for the election was set. A cabinet reshuffle will happen soon, a statement in Mr Bouteflika's name said.
There was no suggestion in the announcement that the president intends to step down before a rescheduled election.
Meanwhile, Algeria's Prime Minister Ahmed Ouyahia announced his resignation and was replaced by Interior Minister Noureddine Bedoui, who has been tasked with forming a new government, the official APS news agency reported.