Smith sang the Dylan classic "A Hard Rain's A-Gonna Fall" on behalf of the American singer-songwriter at the awards ceremony in Stockholm, Sweden.
Stumbling over lyrics at one point, she said, "I apologize. Sorry, I'm so nervous," but the august audience didn't seem to mind in video of the performance on the Nobel Prize Facebook page.
Dylan, 75, is the first songwriter to win a Nobel Prize.
"From an early age, I've been familiar with and reading and absorbing the works of those who were deemed worthy of such a distinction: Kipling, Shaw, Thomas Mann, Pearl Buck, Albert Camus, Hemingway," the speech said.
"These giants of literature whose works are taught in the schoolroom, housed in libraries around the world and spoken of in reverent tones have always made a deep impression. That I now join the names on such a list is truly beyond words."
The Swedish Academy said in October that Dylan had been awarded the 2016 Nobel Prize in literature
for "having created new poetic expressions within the great American song tradition." But days after the announcement, officials said they had given up trying
to reach the iconic musician.
Dylan finally contacted the academy two weeks later, reportedly saying he was "speechless.
Not surprisingly, a prize as coveted as the Nobel usually involves much pomp -- a lavish dinner with the Swedish Academy, a fancy acceptance ceremony, a rousing speech and well-deserved applause.
But Dylan was having none of it. He was busy.
"Pre-existing commitments" is the reason he gave in a letter to the organization, the academy said last month.
Nevertheless, it said Dylan "feels very honored" and wished he could be there in person.
There have been previous Nobel laureates who were unable to attend the ceremony, but the reasons usually involved an illness
or the difficulties of being a political exile
. The academy's only requirement is for Dylan to present a Nobel lecture within six months.
While some purists of literature balked at Dylan's selection, there is little doubt he is a poet whose tunes have spoken to the socially conscious for more than five decades. His 1962 song "Blowin' in the Wind" became an anthem of the civil rights movement.