The ChAdOx1 nCoV-19 vector vaccine (Vaxzevria, AstraZeneca, Cambridge, UK) was developed at Oxford University and is considered safe for the administration in lactating mothers. Nevertheless, as a novel vaccine, there are gaps in the knowledge regarding possible adverse events in breastfeeding infants of vaccinated mothers. This case report provides first-time data on a possible delayed, cutaneous, adverse reaction in a breastfed, 16-month-old female infant after the first administration of the AstraZeneca vaccine to her 33-year-old mother. Even though, no clinical adverse effects were observed in the mother, her daughter had a 2-day rash in the lower extremities and face. The infant’s cutaneous rashes might be a coincidental event. However, all skin lesions were analogous to previous descriptions and photographs of dermatologic reactions, which resolved spontaneously with no medical intervention, in people who had been vaccinated with other COVID-19 vaccines. Our aim is that this short report contributes to the enhancement of parental awareness about the possibility of similar skin rashes in breastfed children when the mothers receive a vaccination and the importance of reporting those adverse reactions to the competent authorities.