The objective of the present study was to determine the subjective impact of the pandemic due to COVID-19 on communication, as perceived by nurses working at emergency services and Intensive Care Units at various hospitals in the Region of Murcia (Spain). A qualitative study was conducted based on the content analysis of 12 semi-structured individual interviews. The participant recruitment process was performed through a snowball sampling technique. Four main dimensions, eleven categories, and two sub-categories were obtained: (1) communication (communicative expressions, both verbal and non-verbal-, and limitations); (2) emotional aspects (positive, negative); (3) overload (first wave, second wave, and third wave); and (4) relationships (health professionals–patients, healthcare professionals, patients–family, and family–health professionals). The main findings of the study show that communication was slightly affected during the pandemic, especially the non-verbal kind, with verbal communication maintained and, in some occasions, strengthened. The lack of training in communication skills and its influence on the management of difficult periods was another important finding. Communication in general deteriorated during the pandemic, especially during the initial waves. Non-verbal communication was more affected due to the use of Personal Protective Equipment and the initial fear of infection, with this finding strongly observed in departments such as emergencies or critical care. The nurses who were interviewed underlined negative emotional aspects associated with a deficit in communication. The positive aspects described were associated with the creation of mutual support spaces and the group cohesion of the work teams during the pandemic. As an implication for current and future clinical practice, we recommend a coordinated institutional response to mitigate the potential emotional effects on workers by designing appropriate communication and emotional expression protocols.