AQAP, which has been labelled the most dangerous branch of the global jihadist network, said France's "Crusader campaign against Islam" has no justification and a "declaration of aggression against Islam and its people."
It said jihad is "more obligatory on the people who are closer" to the fight, in an apparent reference to North African nations and those living in countries helping France.
"Helping the disbelievers against Muslims in any form is apostasy from the religion," it added.
France launched its operation in the African country on January 11 after Mali's interim government requested help. It sent in fighter jets, attack helicopters and ground troops to battle Islamist rebels who had seized the north and were advancing into southern territory.
The campaign racked up a string of early successes as French and African troops drove the extremists from Gao, Timbuktu and the rest of the towns under their control.
AQAP was founded in January 2009 when the Saudi and Yemen branches of the network merged in the south Arabian Peninsula country, and remains active in lawless parts of Yemen despite several military campaigns by Sanaa.