The 37-year-old actor's girlfriend Morena Baccarin, 36, gave birth to a baby girl, who the couple have named Frances Laiz Setta Schenkkan.
The pairs' representative told USA Today: "Morena and Ben are so happy to welcome baby girl Frances Laiz Setta Schenkkan on 2 March.
"All are happy and healthy and appreciate the well-wishes."
Baccarin is already mum to two-year-old Julius with her ex husband Austin Chick.
In February, TMZ reported Baccarin was having a "high risk pregnancy" and she was put on bed rest.
Speaking to PEOPLE Magazine just days before giving birth, the mother said she was finally at a point where she could "just chill".
"Ben is the sweetest," she said. "He's giving me extra TLC and making sure I'm drinking water and taking care of myself.
"I'm right where I should be. All I think about is my son, my family and my future family."
The couple announced they were expecting their first child together in September 2015, just two months after Baccarin and her husband filed for divorce.
McKenzie and Baccarin began dating in 2015 after meeting on the set of 'Gotham'.