A federal appeals court issued an injunction on Wednesday that temporarily blocks President Barack Obama’s Department of Health and Human Services from implementing Obamacare’s contraception mandate.

The mandate requires employers to provide their employees with health care plans that include coverage for contraceptives, sterilization and abortion-inducing drugs.

Missouri business owner Frank O’Brien, who employs 87 people at O’Brien Industrial Holdings, alleged in the lawsuit that led to the injunction that the mandate unconstitutionally infringes on his religious beliefs...