The 46-year-old actor, who is engaged to actress Halle Berry, co-owns Villa Azur, which opened in March this year, reported Daily Mail online.
According to Florida state records, the restaurant was visited by the Department of Business and Professional Regulations for a routine inspection.
Officials discovered 13 violations marked critical, or "likely to directly contribute to food contamination and illness", while seven other violations were deemed "noncritical".
Among the violations listed were fish served raw without having undergone parasite destruction, food thawing in standing water, cutting boards on the floor, food stored on the floor and staff handling ready-to-eat food without gloves.
A Villa Azur spokesperson has played down the concerns, saying, "The kitchen is very clean. We follow all the rules and regulation. We did have an inspection, but the inspector found no major violation."
This comes after Martinez was involved in a brutal brawl with Berry's ex-boyfriend Gabriel Aubry, the father of her four-year-old daughter Nahla on Thanksgiving.