The man was seized on Sunday, September 21, in the restive Tizi Ouzou region in the east, the ministry said.
It did not confirm the authenticity of a video posted on the internet purporting to show the man reading out a statement.
In the video, the man calls on French President Francois Hollande not to intervene in Iraq.
Earlier, militants from the Islamic State (ISIS) group warned they would target France – and other countries – after it launched air strikes against them in Iraq.
The Algerian militant group Jund al-Khilifa, which has pledged allegiance to ISIS, said it carried out the kidnapping, AFP news agency reported, although this has not been confirmed,
An Algerian security official told AP news agency that the kidnap victim was a 55-year-old man who was hiking with two friends when he was abducted.
The area where the Frenchman was taken is a mountainous region, and there have been several kidnappings of Algerian businessmen for extortion in the area.
Most of those who were abducted were later freed by security forces, AFP said.
Al-Qaeda’s North Africa branch, AQIM, and other militant groups are known to operate in Algeria.
On September 22, France lifted the threat level for 30 of its embassies throughout the Middle East and Africa after beginning its first air strikes against IS targets in Iraq on September 19.
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