Muñoz was born to a Puerto Rican family and raised in the Linden projects of East New York, Brooklyn.

[2][4][5] Muñoz's early roles include Ziad in Kari Floren's The Porch at Altered Stages in New York and other off-Broadway productions.

[8][9] Theater critic Robert Feldberg wrote that he preferred Muñoz in the role over Lin-Manuel Miranda, stating that the romance between Usnavi and Vanessa seemed "more believable" and the performance was "emotionally persuasive".

[20] On August 2, 2017, he made a guest appearance in a musical skit on Full Frontal with Samantha Bee,[21] where he played the role of an immigrant affected by Kris Kobach's anti-immigration efforts.

He issued a public apology in April, noting that the phrasing of a tweet caused him to recall an incident where he received anonymous hate mail at his building, leading to fear and distress.