Dixon, who urged the audience not to boo Pence, said the show was performed by "a diverse group of men, women of different colors, creeds and orientations," CNN reported.
Pence had left his seat before Dixon finished his message. But a show spokesman told the AP that Pence stood in the hallway outside the entrance to the auditorium and heard the full remarks.
The vice president-elect's appearance at the Richard Rodgers Theatre in New York triggered both cheers and boos when he slipped into row F in the mezzanine.
"Hamilton," has won 11 Tony Awards and has been praised for depicting the nation’s early years with a multicultural cast. Lin-Manuel Miranda wrote the musical's book, music and lyrics, which blend pop ballads with gospel music and R&B scores.
Pence is in New York with Trump as the team works on presidential transition efforts.
Trump responded to the incident Saturday morning on Twitter, where he called on the cast of "Hamilton" to apologize for their "very rude" treatment of Pence.
Dixon did not waver, standing by his actions as he replied to Trump on Twitter.