Gestation is a crucial life stage for both women and offspring, and outcomes are affected by many environmental factors, including diet. The Mediterranean dietary pattern (MD) is considered a healthy eating pattern that can provide the nutritional requirements of pregnancy. Meanwhile, iron deficiency anemia is one of the most frequent complications related to pregnancy. This study aimed to evaluate how the level of adherence to the MD influences maternal gestational weight gain and specific iron-related maternal biochemical parameters during the pregnancy. Accordingly, an observational, population-based study using data from pregnant women conducted over the entire course of their pregnancy was carried out. Adherence to the MD was assessed once using the MEDAS score questionnaire. Of the 506 women studied, 116 (22.9%) were classified as demonstrating a high adherence, 277 (54.7%) a medium adherence, and 113 (22.3%) a low adherence to the MD. No differences were observed in gestational weight gain among the MD adherence groups but the adequacy of weight gain did vary among the groups, with the proportions of inadequate (insufficient or excessive) weight gain presenting the most notable differences. Total anemia prevalence was 5.3%, 15.6%, and 12.3%, respectively, during the first, second, and third trimesters. For iron-related biochemical parameters, no differences are observed among the adherence groups during pregnancy. With high adherence to the MD as the reference group, the crude odds of iron deficiency diagnosis are significant in the first trimester for both the medium [OR = 2.99 (1.55–5.75)] and low [OR = 4.39 (2.15–8.96)] adherence groups, with deficient adherence to the Mediterranean dietary pattern being responsible for 66.5% (35.5–82.6) and 77.2% (53.5–88.8) of the risk of iron deficiency diagnosis for medium and low adherence, respectively. However, adjusted odds ratios were not significant, possibly due to the small sample size. Our data suggest that MD adherence could be related to gestational weight gain adequacy and that optimal adherence could reduce iron deficiency and/or anemia during pregnancy in the studied population.