COVID-19 vaccines’ safety has been extensively studied; however, further analysis is required in pregnant women, nursing mothers, and breastfed infants. Our aim was to compare the extension and severity of self-reported COVID-19 vaccine side effects in pregnant and breastfeeding women, and breastfed infants. In this cross-sectional study, COVID-19-vaccinated subjects were enrolled using an online survey in Mexico. Women were classified by pregnancy and breastfeeding status at the time of vaccination (n = 3167). After the first or only dose, there was a trend toward fewer systemic effects in pregnant women (p = 0.06). BNT162b2 (Pfizer–BioNTech) had a higher frequency of local symptoms in pregnancy. Lactating women experienced fewer local symptoms after the first or single dose (p = 0.04) and the opposite occurred after the second dose (p = 0.001). ChAdOx1 (AstraZeneca) increased the chances of developing both local and systemic symptoms after the first dose but decreased them after the second dose. The severity was similar across groups, although the result of lack of association in pregnancy requires studies with a larger sample size. Irritability was the most reported symptom in breastfed infants. This study contributes to the knowledge about the side effects in pregnant and lactating women, and breastfed babies.