In the big-screen follow-up to the iconic former television show, Hudson plays the assistant to Parker's character Carrie.
"I just think we were extraordinarily lucky that she was interested," Parker told reporters in New York this week.
Parker said Hudson's character Louise, who is younger and more idealistic than Carrie, "was so necessary to contrast where Carrie is now."
"But it was also very important that we address the one shortcoming on our show, which was we had no women of color and that always concerned me and I talked a lot about that with (writer-director) Michael Patrick (King,)" Parker said, adding that once they decided they wanted the perspective of a 20-something-year-old woman of color in the film, they immediately thought of Hudson.
"At that point, you're like, well, you kind of dream big," Parker said. "It was this wonderful confluence of things that came together."
Hudson, who was once a contestant on "American Idol," won an Oscar for her work in the movie musical "Dreamgirls."