The bill, which took effect last week, bans employers and landlords from discriminating against women who have had an abortion, use contraceptives or are pregnant.
"This bill attacks clinics that help women," Greitens wrote.
The change has been met with opposition from nonprofit "alternative to abortion agencies," sometimes called "pregnancy resource centers," which counsel women against having abortions. Greitens allocated $6 million in funding for such clinics in his 2018 budget proposal.
"Now St. Louis liberals and the National Abortion Rights Action League are trying to undermine and destroy them," Greitens accused.