Trump has "raised serious concerns about the strength of commitment we can expect to see from the United States towards human rights in the future," said Salil Shetty, secretary general of the London-based group.
"He must now put this behind him and both reaffirm and abide by the United States' obligations on human rights, at home and abroad," Shetty said.
Margaret Huang, executive director of Amnesty International USA, criticised "disturbing and, at times, poisonous rhetoric" from Trump in the campaign.
"From internment camps to the use of torture, we have seen disastrous results when those we elect to represent us flout the United States' obligations to uphold human rights," she said.
Trump "must publicly commit to upholding the human rights of all without discrimination".
During a bitter two-year campaign that tugged at America's democratic fabric, the 70-year-old tycoon pledged to deport illegal immigrants and ban Muslims from entering the United States.