Theresa Riggi is serving 16 years in jail for killing her three children at their Edinburgh flat in August 2010.
She is being moved after being attacked twice in recent weeks at Cornton Vale prison, where she was previously held.
Riggi moved to Edinburgh from Skene in Aberdeenshire after the break-up of her marriage to the children's father.
She murdered her three children to death because she feared she would lose them in a battle for custody.
Riggi then tried to commit suicide by throwing herself from a second-floor balcony.