Previous research is inconclusive about when and how job challenge affects innovative behaviour. To address this inconsistency, we primarily draw on the job characteristics theory (JCT) and job demands-resources model (JD-R model) to examine the effect of job challenge on intrinsic motivation and employee innovative behaviour as well as the moderating role of supervisor coaching behaviour. We employ a time-lagged research design to collect data from 318 public sector employees in the UAE. Our finding offers support for a moderated mediation model in which job challenge has a positive and significant effect on innovative behaviour. The study also shows that the association between job challenge and innovative behaviour via intrinsic motivation is stronger under high supervisor coaching behaviour. The findings provide prescriptive insights into the critical role that supervisor coaching behaviours play in clarifying when and how job challenge affects innovative behaviour and indicate relevant managerial implications aimed at encouraging innovative behaviour in the public sector. © 2021 World Scientific Publishing Europe Ltd.