Low vaccine-effectiveness has been recognised as a key factor undermining efforts to improve strategies and uptake of seasonal influenza vaccination. Aiming to prevent disease transmission, vaccination may influence the perceived risk-of-infection and, therefore, alter the individual-level behavioural responses, such as the avoidance of contact with infectious cases. We asked how the avoidance behaviour of vaccinated individuals changes disease dynamics, and specifically the epidemic size, in the context of imperfect vaccination. For this purpose, we developed an agent-based simulation model, and parameterised it with published estimates and relevant databases for population demographics and agent characteristics. Encapsulating an age-stratified structure, we evaluated the per-contact risk-of-infection and estimated the epidemic size. Our results show that vaccination could lead to a larger epidemic size if the level of avoidance behaviour in vaccinated individuals reduces below that of susceptible individuals. Furthermore, the risk-of-infection in vaccinated individuals, which follows the pattern of age-dependent frailty index of the population, increases for older age groups, and may reach, or even exceed, the risk-of-infection in susceptible individuals. Our findings indicate that low engagement in avoidance behaviour can potentially offset the benefits of vaccination even for vaccines with high effectiveness. While highlighting the protective effects of vaccination, seasonal influenza immunisation programmes should enhance strategies to promote avoidance behaviour despite being vaccinated.