Context Despite being a crucial factor in plant growth and fitness, the nutritional requirements of non-native invasive plants are poorly understood and rarely considered when assessing invasion risk; yet, they are particularly relevant in many parts of the world with nutrient-poor soils. Aims We investigated the growth response of a native South American tree species (Tipuana tipu), to soil concentrations of phosphorus (P). T. tipu is widely introduced in some regions of western Australia and South Africa, and we aimed to determine whether soil P availability constrains establishment, naturalisation or invasion of the species. Methods We grew T. tipu (Benth.) Kuntze (Fabaceae), a species that is invasive in some regions, from seed in a glasshouse. All treatments were supplied baseline nutrients, and P from 0 to 640 μg P g−1 dry substrate. Plant height and the number of mature leaves were recorded regularly. Plant biomass, P, and nitrogen (N) concentrations were analysed following destructive harvest. Key results Phosphorus availability had a significant effect on all measured aspects of plant growth. Seed P resources were sufficient to support growth for about 7 weeks, with plants at very low soil P availability (≤5 μg P g−1 dry soil) unable to sustain growth beyond that time. P-toxicity symptoms were observed when substrate P exceeded optimum concentrations (40–160 μg P g−1 dry soil). Conclusions Growth of young T. tipu seedlings was very slow at very low soil P concentrations. Under these conditions, seeds may germinate, and seedlings may survive for a short time, but self-sustaining populations are unlikely to be established. Our study adds to a growing body of research that shows that nutrient requirements of introduced plants and soil nutrient availability influence invasion risk and should be considered in risk assessments for managing species invasions at the landscape level.