Knowledge of Mexican immigrant sleep health is limited. We investigated the association between acculturation, depression, and having trouble sleeping among a nationally representative sample of Mexican immigrant adults. We used a logistic regression model on cross-sectional data from the 2005–2018 National Health and Nutrition Examination Survey on 2,670 non-U.S.-born Mexican adults aged ≥18 years old. Living in the U.S. for ≥10 years (Adjusted Odds Ratio (AOR) = 2.18; 95% Confidence Interval (CI) = 1.39–3.41), speaking majority English (AOR = 1.62; 95% CI = 1.00–2.64), and mild (AOR = 2.70; 95% CI = 1.82–4.02), moderate (AOR = 3.96; 95% CI = 2.53–6.19), and moderately severe/severe (AOR = 5.75; 95% CI = 3.08–10.75) depression levels were associated with having trouble sleeping. Non-U.S. citizenship status was associated with lower odds of having trouble sleeping (AOR = 0.62; 95% CI = 0.43–0.88). Greater acculturation and depression are associated with higher odds of having trouble sleeping. We provide new knowledge on how citizenship status may be linked to the sleep health of Mexican immigrant communities.