Andimi was abducted early January when the insurgents attacked his village.
Days after his abduction, the clergyman, in a video clip released by the insurgents, asked Ahmadu Fintiri, governor of Adamawa, to rescue him.
The sect is yet to confirm the killing of Andimi.
The news comes a week after Islamic State backed Boko Haram released a video to claim it also killed a Christian. The christian was executed by an Islamic State child “soldier” in Borno, Nigeria.
ISWAP also murdered about 11 Christians in December, 2019. The militants said it was part of its recently declared campaign to “avenge” the death of its leader Abu Bakr al-Baghdadi during a US raid in Syria in October.
No details were given about the victims, who were all male, but ISWAP says they were “captured in the past weeks” in Nigeria’s north-eastern Borno State.
One captive in the middle was shot dead while the other 10 are pushed to the ground and beheaded.
“We killed them as revenge for the killing of our leaders, including Abu Bakr al-Baghdadi and [IS spokesman] Abul-Hasan al-Muhajir,” said a member of the group’s media unit, according to Ahmad Salkida, a journalist who was first sent the video.
While reacting to the killings, Nigerian President Muhammadu Buhari condemned the apparent killings and urged Nigerians not to let themselves be divided along religious lines.
“We should, under no circumstance, let the terrorists divide us by turning Christians against Muslims because these barbaric killers don’t represent Islam and millions of other law-abiding Muslims around the world,” he said in a statement.