Home-range size is a key aspect of space-use, and variation in home-range size and structure may have profound consequences for the potential impact of damage and control strategies for invasive species. However, knowledge on home-range structure of naturalized parrot species is very limited. The aim of this study was to quantify patterns of home-range variation according to sex and age of the monk parakeet Myiopsitta monachus, an invasive parakeet in Europe. Mean kernel home-range size was 12.4 ± 1.22 ha (range 1.7–74.1 ha; N = 73 birds). Juveniles had a larger home-range size than adults, but sexes did not differ in kernel home-range size. The mean maximum distance moved by monk parakeets was 727 ± 37.0 m (range: 150–1581 m), and it was not dependent on either the sex or age of the birds. Having a small home range is one of the conditions for the feasible eradication of an invasive species; hence, the small home range of urban monk parakeets that we report here is good news for pest managers. However, this small home-range size can limit the effectiveness of culling operations with traps or feeders with contraceptives or poison, and other alternatives, such as funnel nets or traps, should be used.