The lawsuit, which was filed Wednesday, claims the law violates the First Amendment. The ordinance, however, does not ban NRA-connected contractors from doing business with the city.
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The city says it will defend the law, which went into effect April 1.
Councilman Mitch O'Farrell sought the ordinance in the wake of U.S. mass shootings, including a November attack that killed 12 people at the Borderline Bar and Grill in Thousand Oaks, California. He said the NRA has been a "roadblock to gun safety reform" for decades.
Supporters maintain L.A. shouldn't give public funds to NRA-linked contractors while the city tries to promote gun safety.
NRA attorney Chuck Michel countered that the law would force NRA supporters to drop their memberships for fear of losing their livelihoods.
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"This is modern-day McCarthyism, and my clients are confident no judge will let it stand," Michel said in a statement after the lawsuit was filed.
The legal action asks the court to strike down the law, which it says seeks to "silence NRA's voice, as well as the voices of all those who dare oppose the city's broad gun-control agenda."
The Associated Press contributed to this report.