The COVID-19 lockdown represents a new challenge for mental health researchers and clinical practitioners. This cross-sectional study aimed to investigate the prevalence of depression, anxiety, and perceived stress in postpartum Mexican women. The study included 293, 4–12-week postpartum women over the age of 18. The Edinburgh Postpartum Depression Scale (EPDS), Trait-State Trait Anxiety Inventory (T-STAI), and Ten Perceived Stress Scale (PSS-10), which are all questionnaires validated for the Mexican population, were applied using a web-based online survey. Prevalence and 95% confidence intervals (CIs) were calculated. The mean ± standard deviation (SD) of the maternal age was 29.9 ± 6.3 years; the EPDS score: 11 ± 6, T-STAI score: 41.7 ± 12.3, and PSS-10 score: 17.1 ± 7. The prevalence (95% CI) of the postpartum depression symptoms was 39.2% (34–45%), trait anxiety symptoms were found among 46.1% (32–43%) of the participants, and moderate and high perceived stress were in 58% (52–64) and 10.9% (7.8–15) of the participants, respectively. The prevalence of depressive symptoms, generalized anxiety, and perceived stress was higher among postpartum Mexican women during the COVID-19 outbreak than before the lockdown. Our findings highlight the importance of monitoring perinatal mental health during pandemics and the need to design effective psychologic interventions for these patients.