Emotional intelligence is the key to students’ psychological-social well-being and academic performance, and teachers must provide socioemotional education in the classroom. To achieve this, teachers must display high levels of socioemotional skills that ensure their own personal, social, and career well-being and, as a result, that of their students. This study seeks to gain an insight into the levels of socioemotional skills of emotional perception, emotional understanding, and emotional regulation and how these are linked to the sociodemographic and career profile of teachers in infant and primary education. For this, we surveyed 351 teachers—310 female and 41 male—aged between 20 and 69. We used the Trait Meta-Mood Scale-24 (TMMS-24) together with a questionnaire (ad hoc) to determine the sociodemographic and career profile of participating teachers. Statistical analysis of the data showed that gender impacts on emotional regulation and emotional perception, while age and number of the children were also seen to have significant difference on emotional regulation and emotional perception. In contrast, professional qualifications were only seen to affect emotional perception. The variable reflecting the level at which staff teach showed significant difference on emotional perception and emotional understanding, while administrative posts held by teachers also demonstrated significant difference on their emotional understanding. The results confirm that sociodemographic and work-related variables impact the level of socioemotional skills of infant and primary education teachers. These aspects should be taken into account in the structure and planning of training aimed at developing socioemotional skills in order to ensure their success.