Gourdel was shown squatting on the ground flanked by two hooded men with assault rifles, as he asks for the French president, Francois Hollande, to intervene. He said that he arrived in Algeria on September 20, and was abducted a day later.
"I am in the hands of Jund al-Khilifa. This group is asking me to ask you [Hollande] to not intervene in Iraq. I ask you to do everything to get me out of this bad situation and I thank you."
France launched its first air attacks on IS fighters last week, after joining a US-led coalition to "degrade and destroy" the threat posed by the group.
The French foreign ministry and presidency acknowledged Gourdel had been abducted, and that the video was genuine.
"We will do everything we can to liberate hostages," said France's foreign minister Laurent Fabius. "But a terrorist group cannot change France's position."
Jund al-Khalifa, or "the soldiers of the caliph", are believed to have broken away from the local al-Qaeda affiliate and pledged alliegence to IS. The abduction was announced on the same day IS's spokesman, Abu Mohammed al-Adnani, called on supporters to attack foreigners wherever they are.
In a 43-minute video, Adnani said: "If you can kill a disbelieving American or European - especially the spiteful and filthy French - or an Australian, or a Canadian, or any other disbeliever from the disbelievers waging war, including the citizens of the countries that joined a coalition against the Islamic State, then rely upon God, and kill him in any manner.''
An Algerian security official told the AP news agency that Gourdel, 55, was abducted along with two Algerian friends near Tikdjda, 110km from Algiers.
The Frenchman's companions were released and they alerted authorities about the kidnapping, the security official said.