Prison officials in the city of Multan, where Mrs Bibi is being held, told AFP: "She could be killed by any inmate or even a prison guard, so we have to be careful."
Another said: "We are concerned for her life."
Asia Bibi has been on Pakistan's death row for five years, after she was accused and convicted of blasphemy against the Prophet Muhammad.
She denies the charges, and her sentence has caused international outrage from Christian and human rights groups, including the Vatican.
Various legal appeals and requests for clemency have been turned down.
It also appears that Asia Bibi is dying in prison, as a prison official confirmed her health has deteriorated significantly during her time there.
He said: "She was vomiting blood last month and was having difficulty walking."
