The Burkina government said the pair were kidnapped in Baraboule, near the west African country's borders with Niger and Mali.
A Burkinabe intelligence source told AFP the Australians were a couple in their 80s from the western city of Perth who had lived since 1972 in Djibo, near Baraboule.
Al Qaeda attack on Burkina hotel kills 20
News of the kidnapping came as a militant assault on an upmarket hotel in Burkina Faso's capital Ouagadougou left at least 26 people dead, including many foreigners.
Burkina Faso's Communications Minister Remi Dandjinou said Saturday the couple were Australian nationals, correcting an earlier interior ministry statement identifying them as Austrian.
A spokesman for Malian militant group Ansar Dine, Hamadou Ag Khallini, told AFP in a brief phone message that the couple were being held by jihadists from the Al-Qaeda-linked "Emirate of the Sahara".
He said they were alive and more details would be released soon.
The Australian department of foreign affairs said it was aware of the reports but declined to comment further when contacted by AFP.
"Our post in Accra, Ghana, is working with local authorities on a suspected kidnapping. We will not comment further on the situation," it said.
Al Qaeda calls for lone wolf attacks on West
A European diplomatic source confirmed they had received intelligence on Friday that a Western couple had been kidnapped in Burkina Faso, without giving their nationality.
"According to our information, the kidnappers' objective is to take the hostages towards Mali," the source added, declining to give further details.
A military base in the same region was attacked by militants in August last year, with one Burkinabe policeman killed.
The Emirate of the Sahara is a branch of Al-Qaeda in the Islamic Maghreb (AQIM) operating in northern Mali, according to experts.
AQIM has claimed responsibility for the hotel attack saying it was "revenge against France and the disbelieving West", according to a statement carried by US-based monitoring group SITE.
The attack and kidnapping will heighten concerns that militant groups are casting their net wider in search of targets in west Africa, two months after a siege at a luxury hotel in Mali where 20 people were killed, again mostly foreigners.
Ansar Dine is one of the militant groups that seized control of northern Mali in March and April 2012.
An international military intervention, launched in January 2013, largely drove the militants out, but areas of the north remain beyond the control of Malian and international forces. Militant attacks have spread since the beginning of 2015 towards central and southern Mali.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ