The three aid workers were seized in a refugee camp near Tindouf, Algeria, last October and were then believed to have been transferred to northern Mali, which is now controlled by a mix of Islamist groups.
We have been told that the three hostages have been freed in the region of Gao, Sanda Ould Boumama told Reuters
Boumama said he believed the trio were in the hands of mediators from Burkina Faso, the region's main hostage negotiator.
A MUJWA source, who asked not to be named, confirmed the release but did not give any further details.
There was no immediate comment from Burkinabe mediators, who have led efforts to free a number of Western hostages seized by groups linked to al Qaeda who have collected millions of dollars in ransom payments from the trade in recent years.
Mauritania's ANI news agency reported on its website www.ani.mr that Mamne Ould Oufkir, who had been arrested on suspicion of involvement in the kidnapping was freed overnight.
The agency cited an unnamed informed source saying that Oufkir was transferred to an unknown location.
ANI said the move could have been the first step in process of freeing the Western hostages. It was not clear whether he was a member of MUJWA.