The couple were kidnapped in Baraboule, near the west African country's borders with Niger and Mali.
The incident occurred on the same day as a terror attack struck the nation's capital, in which 23 foreigners were killed at a luxury hotel.
The Al-Qaeda in the Islamic Maghreb (AQIM) militant group has said it carried out the attack, which began on Friday night.
Update: the Foreign Ministry of Burkina Faso updated their statement to clarify that the kidnapped pair were Australian and not Austrian as first thought.
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The Austrian foreign ministry has updated its advice for the country to recommend extreme caution for visitors to the country, and to avoid the central city.