One of her legs and several fingers were removed in the attack on Tuesday.
Albinos have suffered widespread persecution in Tanzania, where witch doctors say magic potions made with albino body parts can bring good luck.
Such killings have declined in recent years, but this latest attack has prompted a human rights group to call for all witch doctors to be banned.
At a press conference on Wednesday, the group, Under The Same Sun said the current regulation of witch doctors was clearly not working.
The attack occurred in the village of Gasuma, in Simiyu province – a remote rural area in the north-west of the country where there have been killings of albinos before, our reporter says.
The woman’s left leg, two fingers from her left hand and a nail from one of her thumbs were removed.
According to Under the Same Sun, which campaigns against the discrimination of people living with albinism, the last killing of an albino in Tanzania was in February 2013.
In recent years, the government has been also been trying to address the problem, and an albino MP was appointed several years ago.