A statement from Bouteflika's office made the announcement but gave no reason for the changes which come as Algeria faces an economic crisis because of falling oil revenues.
Noureddine Boutarfa, an engineer who headed the powerful state electricity and gas company Sonelgaz for a decade, took over the energy ministry from Salah Khebri.
Haji Baba-ammi, a minister of state in charge of budget affairs, was promoted and given the finance ministry, replacing Abderahmane Benkhlafa.
Both Khebri and Benkhlafa had been appointed in May last year in another surprise reshuffle.
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The reshuffle is Bouteflika's third since his re-election to a fourth five-year term in 2014.
It comes weeks after the 79-year-old leader returned from Switzerland after undergoing what the presidency called "routine medical checks".
Bouteflika suffered a stroke in 2013 that has impeded his mobility and speech.
Algeria, a member of the OPEC oil cartel, has been hit hard by weaker oil prices and its foreign reserves have fallen.
The International Monetary Fund said this week the value of oil and natural gas exports in the six Gulf Cooperation Council countries and Algeria is projected to fall by almost USD 450 billion this year compared to 2014.