Evidence suggests that non-binary people have poorer mental and physical health outcomes, compared with people who identify within the gender binomial (man/woman). Research on the impact of the COVID-19 pandemic on mental health has been conducted worldwide in the last few months. It has however overlooked gender diversity. The aim of our study was to explore social and health-related factors associated with mental health (anxiety and depression) among people who do not identify with the man/woman binomial during COVID-19 lockdown in Spain. A cross-sectional study with online survey, aimed at the population residing in Spain during lockdown, was conducted. Data were collected between the 8th of April until the 28th of May 2020, the time period when lockdown was implemented in Spain. Mental health was measured using the Generalised Anxiety Disorder 7-item (GAD-7) scale for anxiety, and the Patient Health Questionnaire (PHQ-9) for depression. The survey included the question: Which sex do you identify with? The options "Man", "Woman", "Non-binary" and "I do not identify" were given. People who answered one of the last two options were selected for this study. Multivariate regression logistic models were constructed to evaluate the associations between sociodemographic, social and health-related factors, anxiety and depression. Out of the 7125 people who participated in the survey, 72 (1%) identified as non-binary or to not identify with another category. People who do not identify with the man/woman binomial (non-binary/I do not identify) presented high proportions of anxiety (41.7%) and depression (30.6%). Poorer mental health was associated with social-employment variables (e.g., not working before the pandemic) and health-related variables (e.g., poor or regular self-rated health). These findings suggest that social inequities, already experienced by non-binary communities before the pandemic, may deepen due to the COVID-19 pandemic.