Diversity and psychological health issues at the workplace are pressing issues in today's organizations. However, research linking two fields is scant. To bridge this gap, drawing from team faultline research, social categorization theory, and the job-demands resources model, we propose that perceiving one's team as fragmented into subgroups increases strain. We further argue that this relationship is mediated by task conflict and relationship conflict and that it is moderated by psychological empowerment and task interdependence. Multilevel structural equation models on a two-wave sample consisting of 536 participants from 107 work teams across various industries and work contexts partially supported the hypotheses: task conflict did indeed mediate the positive relationships between perceived subgroups and emotional exhaustion while relationship conflict did not; effects on stress symptoms were absent. Moreover, contrary to our expectations, neither empowerment, nor task interdependence moderated the mediation. Results indicate that team diversity can constitute a job demand that can affect psychological health. Focusing on the mediating role of task conflict, we offer a preliminary process model to guide future research at the crossroads of diversity and psychological health at work.