"As for the blessed Battle of Paris, we, the Organisation of al Qaeda al Jihad in the Arabian Peninsula, claim responsibility for this operation as vengeance for the Messenger of God," said Nasser bin Ali al-Ansi, a leader of the Yemeni branch of al Qaeda (AQAP) in the recording.
Gunmen killed a total of 17 people in three days of violence that began when they opened fire at Charlie Hebdo in revenge for its past publication of satirical images of the Prophet.
Ansi, the main ideologue for AQAP, said the "one who chose the target, laid the plan and financed the operation is the leadership of the organisation", without naming an individual.
He added without elaborating that the strike was carried out in "implementation" of the order of overall al Qaeda leader Ayman al-Zawahri, who has called for strikes by Muslims in the West using any means they can find.
AQAP itself is led by Nasser al-Wuhayshi, who is also Zawahris number two in the networks global hierarchy.
"We did it in compliance with the command of Allah and supporting His Messenger, peace be upon Him," Ansi added.
It was not immediately possible to verify the authenticity of the recording, which carried the logo of the al Qaedas media group al-Malahem.
The first edition of Charlie Hebdo published after last weeks attacks sold out within minutes at newspaper kiosks around France on Wednesday, with people queuing up to buy copies to support the satirical weekly.(*)