Royal Caribbean Cruises Ltd. served seafood contaminated with a neurotoxin that severely sickened a passenger, a new lawsuit alleges.

The May 16 complaint filed by Dawn Williams raises the unusual claim that fish she ate aboard RCCL’s Radiance of the Seas last year was contaminated with ciguatera, a neurotoxin accumulated by some fish from their consumption of microalgae living on or near coral reefs.

Symptoms of the disease—which is most often carried by barracuda, grouper, snapper, and mackerel—can cause nausea,...