America's next president demanded an apology from the cast over the public appeal at the end of a performance of the hit musical.
Mr Pence had been booed by audience members during the show, and an actor then read an open letter pleading with him to represent “diverse America”.
"Our wonderful future VP Mike Pence was harassed last night at the theater by the cast of Hamilton, cameras blazing," the billionaire businessman wrote. "This should not happen!"
He then added in a second tweet: "The Theater must always be a safe and special place. The cast of Hamilton was very rude last night to a very good man, Mike Pence. Apologize!"
The President-elect was supported by longtime ally and Speaker of the House Newt Gringrich, who condemned the actors, saying they had behaved with "arrogance" and shown "hostility" to the future Vice President.
Yet the cast member who addressed Mr Pence, Brandon Dixon, responded to Mr Trump's remarks saying: "Conversation is not harassment, sir."
He struck a respectful tone when addressing the Indiana Governor from the stage.
“Vice President-elect Pence, we welcome you and truly thank you for joining us here," he said.
“We sir, 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.
“But we truly hope this show has inspired you to uphold our American values and to work on behalf of all of us. All of us.”
The Vice President-elect was on his way out when Mr Dixon started his announcement, but he heard the plea in the hallway, the Associated Press reported.
An evangelical Christian, Mr Pence has repeatedly taken an anti-LGBT stance, saying businesses should have the right to discriminate against gay people on the grounds of religion.
And the impassioned plea to him, made by an African-American actor in front of a ethnically diverse cast, comes after Donald Trump vowed to deport three million undocumented immigrants immediately on taking office.
On Twitter, audience members pointed out the irony of a staunch conservative with such views attending a hip hop musical with a majority non-white cast, whose lead actor Javier Muñoz is openly gay and HIV positive. Mr Muñoz has been at the forefront of the fight against stigma around HIV and Aids.
Some conservative commentators said the reaction to Mr Pence was disrespectful, and claimed it represented the reaction of the out-of-touch “elite”, since tickets to the show reportedly cost hundreds of dollars.
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