Justices Samuel Alito, Neil Gorsuch and Clarence Thomas dissented. Justice Brett Kavanaugh issued a concurring opinion.
The case, as well as several others service members have filed in other districts, created questions about whether courts would limit, if not overturn, the military's COVID-19 mandate.
Legal experts have been skeptical that the lawsuits would succeed, despite the initial injunctions won by the SEALs.
In that case, more than 30 Navy special forces members -- mostly SEALs -- claimed that their efforts to obtain religious waivers to avoid getting vaccinated "are futile because denial is a predetermined outcome," according to court filings.
Kavanaugh, in his concurring opinion, simply noted that he sees "no basis in this case for employing the judicial power in a manner that military commanders believe would impair the military of the United States as it defends the American people."
In writing his dissent, Alito compared the request of the Navy SEALs to that of the death row inmate who petitioned the high court to let his pastor lay hands on him and pray aloud as part of his execution.
Alito also expressed concern over the fact that, in his eyes, "the ruling essentially gives the Navy carte blanche to warehouse [the SEALs] for the duration of the appellate process, which may take years."
The decision may also impact other cases filed against the Defense Department over the vaccine requirement, including a potential class-action suit filed in Florida by 30 unnamed officers and service members seeking relief from the order.
The judge in that case ruled that the Navy cannot remove one of the plaintiffs, a destroyer commander, for refusing the COVID-19 vaccine.
-- Konstantin Toropin can be reached at firstname.lastname@example.org. Follow him on Twitter @ktoropin.