Syndicated columnist Liz Smith reported Friday that Parker, 37, is pregnant, and is due to give birth in the fall. Parker's publicist wasn't immediately available for comment.
The 40-year-old Broderick, who recently co-starred on Broadway in "The Producers," and Parker, co-star of HBO's "Sex and the City," have been married since May 1997.
As a result of the pregnancy HBO is temporarily shutting down production on the award-winning program for a little while as it figures out how to work around Parker's pregnancy.
The new season for her show was scheduled to start in June. That's been pushed back to July.