Health insurance start-up Oscar Health sued Florida Blue on Tuesday, accusing the independent licensee of the Blue Cross and Blue Shield Association of illegally running a monopoly in the state's Obamacare market.

Oscar Health accused Florida Blue of using "exclusive policy" agreements that prevent insurance brokers from selling Oscar health coverage plans or other insurance if they already sell Florida Blue's policies.

The "scheme," Oscar Health said, is "devastating" for newcomers like the company and, if allowed any further will limit "consumer choice" and undermine "the role of brokers." Joshua Kushner, brother to Trump adviser Jared Kushner, co-founded Oscar Health.

"Florida Blue wrongfully uses its monopoly power to compel brokers to sell only its plans when industry standards require independent brokers to find the best options for consumers' needs," Oscar Health said in a lawsuit filed Tuesday in federal court in Florida.

A spokesman for Florida Blue said the company is reviewing the complaint but added there is "no merit" to Oscar Health's claims.

"Contracted agents are independent contractors," Florida Blue spokesman Paul Kluding told CNBC. "They have the choice to contract with whichever carriers they choose. Likewise they are free to choose to contract with carriers that operate on an exclusive basis, or to choose carriers that do not."

"There is also nothing about the Florida market which precludes any competitor," he added.

Florida Blue is the largest provider in the state of plans under the Affordable Care Act, more commonly known as Obamacare, serving more than 5 million members across the state.

Oscar Health, which ranks No. 12 on the 2018 Disruptor 50 List, began offering individual health plans in Orlando for the first time this year. Its investors include Google parent Alphabet.

Oscar distinguishes itself from much larger rivals, including UnitedHealth, with its millennial-focused subway ads and iPhone apps for members to book appointments and get advice from doctors.

—CNBC's Christina Farr contributed to this report.