"Every American, including family business owners like the Greens, should be free to live and do business according to their religious beliefs," Kyle Duncan, general counsel for the Becket Fund for Religious Liberty, said in a statement.
The morning-after pill works by preventing ovulation or fertilization. In medical terms, pregnancy begins when a fertilized egg attaches itself to the wall of the uterus. If taken within 72 hours of unprotected sex, it can reduce a woman's chances of pregnancy by as much as 89 percent.
Critics of contraception say it is the equivalent of an abortion pill because it can prevent a fertilized egg from attaching to the uterus. The lawsuit also alleges that certain kinds of intrauterine devices can destroy an embryo by preventing it from implanting in a woman's uterus.
Hobby Lobby is the largest business to file a lawsuit against the mandate.
Hobby Lobby calls itself a "biblically founded business" and is closed on Sundays. Founded in 1972, the company now operates more than 500 stores in 41 states and employs more than 13,000 full-time employees who are eligible for health insurance coverage. The company, which is self-insured, has said it will face a daily $1.3 million fine beginning Jan. 1 if it ignores the law.
"It is by God's grace and provision that Hobby Lobby has endured," said David Green, founder and CEO. "Therefore we seek to honor God by operating the company in a manner consistent with biblical principles."
The Green family has said it has no moral objection to the use of other contraceptives and will continue covering them for its employees.