The COVID-19 pandemic undoubtedly burdened families, perhaps even more for parents of children with neurodevelopmental disabilities. This research aims to determine the anxiety levels in mothers of children with neurodevelopmental disorders (autism spectrum disorder and specific language impairment) and mothers of typically developed children. The cross-sectional study comprised 280 mothers from the period of the COVID-19 pandemic in Serbia. A confidential survey included main demographic data and the State-Trait Anxiety Inventory (STAI). Results revealed that the mean levels of STAI-S and STAI-T are elevated in the observed sample of mothers in the first pandemic wave; the STAI-S level is in the high category (STAI-S mean = 46.69), while STAI-T is in the intermediate category near the cut-off value for the high level (STAI-T mean = 43.04). A statistically significant strong positive correlation between STAI-S and STAI-T is seen (r = 0.802, p = 0.001). GLMM analysis revealed that interactions, rather than independent variables, significantly impact anxiety, implying a complex relationship between the observed variables and STAI. Compared with the results from the pre-pandemic study, our findings reveal that COVID-19 affects mothers of children with and without neurodevelopmental disorders in a complex manner, imposing a need for psychological support, which may positively affect mothers’ mental health and the development of their offspring.