He graduated from The Danish National School of Theatre as a director in 1974. He has been hired by various Danish theaters as either an actor or a director; as an actor, he is most often cast as the villain in productions. In 1978, he got his first movie role in the movie Slægten. His credits in Danish television series, include Bryggeren, Forsvar, Forbrydelsen and many others. His voice-over credits include John Silver in Treasure Planet, Ice Age: The Meltdown and others.
He has been nominated for several Danish theater and movie awards. Munk has also translated over 30 plays for Danish theaters over the years.