After what he thought was a disappointing audition with Allen, Mortensen said he learned that he won a part.
"Next day my agent calls me and said, 'He loves you. You got a part.' 'Oh really? What's the part?' He goes, 'I don't know exactly, but it's a part. You're in the movie,'" Mortensen said.
When he arrived at the set on Long Island, New York, Mortensen said he still had no idea what his role was. After sometime, he and another actor were called in to do a scene.
"They have this big huge party. It looks fantastic, lights, all this stuff. And Woody Allen is whispering into this actor's ear, this other actor who's been called. And the actor smiles and nods," Mortensen said. "He goes, 'Okay, let's shoot.' And I go, 'Mr. Allen? Sir? What am I supposed to do?' 'You just follow his lead. You'll be alright.' And I'm freaking out. I have no idea what the story's about."
Mortensen said he improvised some lines, and the next day, he told his agent he thought it went "pretty good."
"And of course the movie comes out the next fall or whatever, and I told my family, 'Friday.' And I'm not in it. I'm not in the credit, nothing," Mortensen laughed.
Since then, Mortensen went on to become a leading man. In "Captain Fantastic," he plays Ben, a father who lives off the grid with his six children.
Mortensen, who has one son in real life, bonded with his on-screen children in preparation for the film.
"Couple of weeks before we started shooting, [we got] to know each other, to work on the skills that we show in the movie -- the things that we do together: rock climbing, martial arts, music," Mortensen said. "What was great was we got to know each other that way and so that was a great way to do it, all these activities that we did together."
Mortensen calls his character one of the best roles he's ever undertaken.
"I don't think I've ever played a role that's been this complex or that's had this fulfilling an emotional journey, and it's one of the best roles, if not one of the most complete I've ever done," he said.
Watch Viggo Mortensen's full interview with Peter Travers on ABC News' "Popcorn With Peter Travers" above.