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.
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.