Militants have freed an Australian woman kidnapped with her husband last month in Burkina Faso, releasing her in neighbouring Niger.

Jocelyn Elliott and her husband Ken, who are in their 80s, were snatched from Djibo near the border with Mali.

The couple had provided medical services in the town since the 1970s.

Al Qaeda-linked militants said the kidnapping was an attempt to secure the release of imprisoned fighters, a jihadist monitoring group said.

The group, al Qaeda in the Islamic Maghreb (AQIM), said in an audio recording that it would release Mrs Elliott so as "not to make women involved in the war", according to a translation made by the SITE Intelligence organisation.

Mrs Elliott appeared alongside Niger's President Mahamadou Issoufou in the town of Dosso, Niger's presidential spokesman said.

Efforts to free her husband were continuing, the spokesman added.

Australia's Prime Minister Malcolm Turnbull confirmed that the Australian government had been in contact with Mrs Elliott following her release.

The couple were kidnapped on the same day as a deadly attack on a hotel in the Burkina Faso capital Ouagadougou, which was also claimed by AQIM.

In response, local people in Djibo launched a social media campaign calling for their release.