The implementation of robots in tourism services is transforming how companies interact with their customers and create value. Although corporate initiatives are beginning to focus on proactive robot services, little is known about the impact of this behavioural characteristic of service robots on customer value co-creation. Through two experiments and one field survey, this research demonstrates that customers’ co-creation intention is higher when a robot’s service proactivity is high (vs. low), and that this relationship is mediated by perceived robotic empathy. Furthermore, customer task orientation negatively moderates the mediating effect of empathy perception that underlies the relationship between service proactivity and customers’ co-creation intention. These findings provide new insights into the effect of service robots’ behavioural characteristics on customer–robot interactions.