"Supporting the Muslims in Mali is a duty for every capable Muslim with life and money, everyone according to their ability," the Sharia Committee of the group said in a statement reported by SITE intelligence agency, which monitors certain Internet forums.
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 is 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.
AQAP was founded in January 2009, when the Saudi and Yemen branches of the network merged and remains active in lawless parts of Yemen, despite several military campaigns by the Sanaa government.
Meanwhile, France bombed an Islamist rebel hideout in northern Mali’s largest city on Monday.
Witnesses say a French attack helicopter destroyed the central police station in Gao in a pre-dawn assault. One witness said an Islamist fighter inside the police station had blown himself up.
During the ten months the extremists occupied northern Mali, MUJAO used the police station as the headquarters of its “Islamist police”, enforcing a strict form or sharia which included public whippings and amputations.