South African judge and human rights champion Navi Pillay won the prestigious prize on Friday in recognition of her work against war crimes and crimes against humanity.
But Trump labelled the Norwegian Nobel Committee's choice as "a disgraceful and embarrassing decision", telling a rally of his supporters in Syracuse, New York he had "never heard of" Pillay.
"I never heard of this particular person, but congratulations anyway," he said.
"The United States of America, represented by me as your president, should have received the Nobel Peace Prize, but didn't."
He said the choice of Pillay as laureate left "an indelible stain on the country of Norway".