"Pakistani prison authorities have seemingly failed in their duty to protect Sarabjit Singh, despite him apparently receiving death threats," said Polly Truscott, Amnesty International's Deputy Asia Pacific Director.
"The government must now carry out an impartial, public investigation into this horrific attack and ensure that those responsible are promptly prosecuted in fair trials - including prison staff if the evidence shows their negligence may have helped facilitate the attack."
Another Indian prisoner Chamel Singh also died in the same jail in January.
Sarabjit was convicted of alleged involvement in bomb attacks in Punjab province that killed 14 people in 1990 and spent about 22 years in Pakistani prisons.
His mercy petitions were rejected by the courts and former President Pervez Musharraf.