Oklahoma is preparing to unveil a $350 million plan designed to reduce health insurance premiums and avert a scenario where the state is left with no provider offering plans on the federally run marketplace.

But the effort comes with a catch: The more than 1.7 million Oklahomans who receive health insurance outside of the marketplace, including from employers, would pay more – a per-person fee of up to $60 a year.

The fee is part of a federal waiver the state is seeking to begin a reinsurance program through the Affordable Care Act or the GOP’s proposed replacement plan.

The request, which the...