Pregnant women can enjoy sablefish as part of the six six-ounce servings of moderate mercury cooked seafood they eat per month. The FDA recommends a limit on the amount and kind of seafood pregnant women ingest to prevent harm to themselves and their baby caused by high levels of mercury. Sablefish is in the class of fish considered to have a moderate amount of mercury according to the American Pregnancy Association. Additionally, pregnant women should only eat sablefish if it is fully cooked. According to the FDA, pregnant women should not eat any raw or undercooked seafood and should cook fish to at least 145°F.