An Australian woman kidnapped by terrorists in west Africa has been freed.

Jocelyn Elliott has been released but husband Ken, who volunteered his services in the country as a doctor, is still being held by a group linked to al-Qaeda.

She was let go on the orders of al-Qaeda, which reportedly told the Islamic militants responsible that women should not be involved in war.

Australian Prime Minister Malcolm Turnbull said the woman's release is welcome news.

"We want to thank the government of Niger and the government in Burkina Faso which is of course where the Elliott's were living when they were kidnapped and we want to thank them for the work that they're doing."

The Elliotts are in their eighties.