The woman, 53, was travelling south of the city of Djanet, close to the borders with Niger and Libya, Algerian newspaper Echorouk reports.
She has probably been taken by her captors into Niger, it says.
She was reportedly kidnapped with her driver and guide by a group of 14 men riding in two trucks.
She arrived in the country on 20 January for a month-long holiday, Echorouk adds.
There was no suggestion that the abduction was linked to recent anti-government unrest in Algeria.
Nor was there any immediate claim of responsibility but it comes in a region where the kidnapping of foreign nationals has caused increasing alarm.
Troops on alert
The woman was abducted on Wednesday at about 1800 (1700 GMT) in Alidem, an area 130km (80 miles) south of Djanet, a security source told AFP news agency.
The driver and guide who were with her were freed and told investigators they had been kidnapped by “14 men riding in two Toyota trucks”.
Troops in the Alidem region have been put on alert and are searching for the vehicles.
But the abductors have probably already left the country, the source added.
Last year, Algeria, Niger and fellow Sahara states Mauritania and Mali set up a joint military headquarters in the south of Algeria to improve co-ordination in combating one of the most powerful militant groups in the region, al-Qaeda in the Islamic Mahgreb (AQIM).
The group, which emerged in 2007 from an Algerian militant group, carries out kidnappings for ransom or to demand the release of prisoners as part of its activities.
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