Background: Although current guidelines recommend that mothers with suspected or confirmed SARS-CoV-2 infection should be encouraged to initiate and continue breastfeeding, up-to-date literature shows conflicting data regarding breastfeeding experiences in infected women. This survey aimed to report on the psychological impact of SARS-CoV-2 infection on breastfeeding practice and medical counselling in a single tertiary center in Southern Italy. Methods: One-hundred breastfeeding women with SARS-CoV-2 infection at delivery were given an anonymous questionnaire regarding breastfeeding and women’s perception of the impact of COVID-19 on breastfeeding. Results: 75% of women reported they had difficulty breastfeeding; among them, 66 (66%) declared that separation from their babies after delivery affected their ability to breastfeed. Incidence of reported difficulties in breastfeeding was higher in women who underwent caesarean section compared to women with vaginal delivery (56/65, 86.2% vs. 19/35, 54.3%, χ2 = 12.322, p < 0.001) and in women with a hospital stay of more than 5 days (48/57, 84.2% vs. 23/37, 62.2%, χ2 = 5.902, p = 0.015). Furthermore, the incidence of difficulties in breastfeeding was higher in women who subsequently decided to use exclusively infant formula compared to women who mixed maternal milk with infant formula and women who breastfed exclusively with maternal milk (48/49, 98% vs. 20/25, 80% vs. 7/26, 26.9%, χ2 = 46.160, p < 0.001). Conclusions: Our survey highlights the importance of healthcare support and information on hygiene practices to decrease the perceived stress related to breastfeeding for infected mothers under restrictions, especially in women undergoing cesarean section and with a long hospital stay.