The group stated the case against five senior officers in a new 133-page report based on hundreds of interviews, including with military sources, and using leaked defence ministry documents.
The allegations centre on thousands of people Amnesty claimed were extra-judicially murdered by the security forces and its civilian vigilante allies, as well as crimes against those held in military custody.
Amnesty's secretary general Salil Shetty described the abuses as "sickening" but Nigeria's military hit back saying the report was designed to besmirch its reputation.
Nigerian forces "have committed countless acts of torture; hundreds, if not thousands, of Nigerians have become victims of enforced disappearance; and at least 7,000 people have died in military detention as a result of starvation, extreme overcrowding and denial of medical assistance", it added.
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Amnesty said commanders based in the northeast "should be investigated for potential responsibility for war crimes of murder, enforced disappearances and torture".
The ICC in The Hague has previously opened a preliminary investigation into the Boko Haram conflict, which Amnesty said has killed at least 17,000 people since 2009.
The tribunal has however stated there was insufficient evidence tying Nigeria's military to systematic and orchestrated atrocities targeting civilians.
But the report said: "Amnesty International believes that the evidence contained in this report and submitted separately to the (ICC) Office of the Prosecutor is sufficient to reopen this issue.