A statement from the organization, based in London, said the three men, each convicted of murder, could be executed as early as Thursday evening by firing squad.
Indonesia resumed executions in March after a four year hiatus.
"More executions in Indonesia must be stopped," said Papang Hidyat, Amnesty International's Indonesia researcher. "They call into question many of the human rights reforms and commitments made by the Indonesian government in recent years. Where it seemed that President (Susilo Bambang) Yudhoyono, who is due to step down next year, would leave a positive legacy relating to human rights, the opposite now appears to be the case."