1570s, "a ruling authority's pardon of past offenses," from French amnistie "intentional overlooking" (16c.), from Latin amnestia, from Greek amnestia "forgetfulness (especially of wrong); an amnesty," from amnestos "forgotten; forgetful," from a- "not" (see a- (3)) + mnestis "remembrance," which is related to mnaomai "I remember," from PIE root *men- (1) "to think."
Usually specifically of pardons or offers of pardon for a class of offenses against a government. As a verb from 1809. The non-governmental organization Amnesty International was founded 1961 to call attention to the plight of prisoners of conscience, as Appeal for Amnesty; the name was changed 1963.