U.S. District Judge Joe Heaton ruled last month that Hobby Lobby must comply in spite of its belief that the "morning-after pill" induces abortion.
On Thursday, the appeals court agreed that the mandate did not appear to substantially burden religious exercise in the case.
The panel quoted a portion of Heaton's opinion to deny Hobby Lobby's motion for an injunction.
"The particular burden of which plaintiffs complain is that funds, which plaintiffs will contribute to a group health plan, might, after a series of independent decisions by healthcare providers and patients covered by [the corporate] plan, subsidize someone else's participation in an activity that is condemned by plaintiff[s'] religion. Such an indirect and attenuated relationship appears unlikely to establish the necessary 'substantial burden,'" Heaton wrote.
The appeals court has yet to rule on the merits of the case.
More than 40 suits have been filed against the Obama policy on behalf of more than 100 plaintiffs.
Hobby Lobby's action also involves Mardel, a chain of Christian bookstores owned by the same family, the Greens.