Moore dropped out of the movie about 1970s porn star Linda Lovelace this week after a trip to the hospital for undisclosed reasons.
Her publicist has since said Moore is being treated for exhaustion after the stressful breakup of her six-year marriage to actor Ashton Kutcher.
"Mamma Mia!" star Amanda Seyfried plays the title character in "Lovelace," which began filming last month in Los Angeles, People.com noted.
Parker is best known for her work in the "Sex and the City" TV series and film franchise.
Celebrity Families of 2014 [PHOTOS]