Crisis situations require employees to be adaptive and proactive in order to be successfully managed. Because servant leaders focus on serving their followers, they should be able to fulfill their followers’ needs and respond appropriately to situations that cause uncertainty, thereby helping them manage crises. Against this backdrop, we investigated whether the perception of servant leadership can support follower adaptivity and proactivity in a crisis context. Additionally, we examined two potential mediating processes to explain these relationships (i.e., followers’ basic psychological need satisfaction and procedural justice perceptions). Using a longitudinal study with three measurement points between March 2020 (at the beginning of the COVID-19 crisis) and October 2020, we surveyed 129 teachers employed at several schools in a private school association in Germany. In line with our hypotheses, the results of the path analysis showed that servant leadership perceptions were positively associated with both mediators. The relationships between servant leadership and followers’ proactivity and adaptivity were mediated by basic need satisfaction. However, contrary to our assumptions, we found no direct associations between servant leadership and follower behavior, no indirect relationship between servant leadership and adaptivity via procedural justice, and even a negative indirect relationship between servant leadership and proactive behavior via procedural justice. Based on our findings, we discuss the potential benefits and negative implications of servant leadership in the crisis context.