The fraction of absorbed photosynthetically active radiation (fAPAR) is a key parameter for estimating the gross primary production (GPP) of trees. For continuous, dense forest canopies, fAPAR, is often equated with the intercepted fraction, fIPAR. This assumption is not valid for individual trees in urban environments or parkland settings where the canopy is sparse and there are well-defined tree crown boundaries. Here, the distinction between fAPAR and fIPAR can be strongly influenced by the background and large illumination variations due to multi-scattering and shadows of buildings. This study investigates the radiative budget of PAR bands using a coupled leaf-canopy radiative transfer model (PROSPECT-DART), considering a suite of tropical tree species over a wide range of assumed leaf chlorophyll contents. The analyses simulate hyperspectral images (5 nm bandwidth) of individual tree crowns for the selected background (concrete vs. grass) and illumination conditions. We then use an artificial neural network-based method to partition sunlit vs. shaded leaves within each crown, as the latter have lower fAPAR and fIPAR values. Our results show fAPAR of sunlit leaves decreases with the ratio of diffuse to direct scene irradiance (SKYL), while SKYL has minimal influence for shaded leaves. Both fAPAR and fIPAR decrease at more oblique solar zenith angles (SZA). Higher values of fAPAR and fIPAR occur with concrete backgrounds and the influence of the background is larger at higher diffuse ratio and solar zenith angles. The results show that fIPAR is typically 6–9% higher than fAPAR, and up to 14% higher for sunlit leaves with a concrete background at SKYL = 0. The differences between the fIPAR and fAPAR also depend on the health condition of the leaves, such as chlorophyll content. This study can improve the understanding of urban individual trees fAPAR/fIPAR and facilitate the development of protocols for fAPAR field measurements.