In the last two years, the obligatory use of technologies due to the COVID-19 pandemic has increased the technostress suffered by education professionals. This study investigates the relationships between technostress and perceived organizational support and the influence of certain socio-demographic variables. An online survey was administered to 771 teachers working in different educational stages in various autonomous communities in Spain. Perceived organizational support was found to be significantly correlated with technostress. Women tend to experience more technostress in general and significant gender differences were also found in the dimension of anxiety. The analyzed data also suggest that perceived organizational support is higher in private schools. In urban centers, teachers’ technostress increases in higher educational stages, such as secondary education and baccalaureate. Further work is needed to develop school policies that address the needs of teachers and provide support for those at risk of technostress. In addition, there is a need to design coping strategies and prioritize the most at-risk sectors to improve their overall health and well-being.