At the end of the Broadway show, the cast addressed the Republican from the stage and delivered a message to the incoming administration of Donald Trump.
“We are the diverse America, who are alarmed and anxious that your new administration will not protect us, our planet, our children, our parents or defend us and uphold our inalienable rights," said actor Brandon Victor Dixon, who plays Aaron Burr, the nation's third vice president.
Mr Pence moved to leave before Dixon finished the unprecedented message. But a show spokesman said he stood in the hallway outside the entrance to the auditorium and heard the full remarks.
The vice president-elect had endured jeers and boos - and just a smattering of cheers - from the moment he had entered the theatre.
At one point the actors had to pause during a song while audience members jeered the Republican governor. One theatre-goer also reported there was extended applause during the play at the line: "Immigrants, we get the job done'".
Mr Trump, whose victory in last Tuesday's election triggered protests across the US, sparked concern during the campaign with a series of controversial pledges as part of a crackdown on immigration.
The reaction of the audience towards Mr Pence divided social media users.
"Pence getting booed at Hamilton bums me out. Whatever you think of him. He’s trying to engage. Could get ideas from far worse places," New York Times reporter Dave Itzkoff wrote on Twitter.
Many others said he deserved the treatment because of his stance on issues such as gay rights. John Aravosis, an LGBT advocate, tweeted: "You know what's worse than getting booed? Every single thing Mike Pence stands for."
Mr Pence has faced fierce criticism for his position on gay rights. As Indiana governor, he signed the Religious Freedom Restoration Act into law in 2015.
Advocates said it would expand “religious liberty” by allowing business owners to push back when government policy was in conflict with their beliefs. But opponents said the law was discriminatory against lesbian, gay, bisexual and transgender individuals.
Hamilton, which has won 11 Tony awards, has proved to be an unlikely Broadway smash about the life and times of Alexander Hamilton, the first United States Secretary of the Treasury and one of America’s “founding fathers”, as re-enacted by a non-Caucasian cast, using rap and hip-hop to tell his story.