Aims. We performed a spatially resolved spectral X-ray study of the pulsar wind nebula (PWN) in the supernova remnant G0.9+0.1. Furthermore, we modeled its nonthermal emission in the X-ray and very high-energy (VHE, E > 100 GeV) γ-ray regime. Methods. Using Chandra ACIS-S3 data, we investigated the east-west dependence of the spectral properties of G0.9+0.1 by calculating hardness ratios. We analyzed the EPIC-MOS and EPIC-pn data of two on-axis observations of the XMM-Newton telescope and extracted spectra of four annulus-shaped regions, centered on the region of brightest emission of the source. A radially symmetric leptonic model was applied in order to reproduce the observed X-ray emission of the inner part of the PWN. Using the optimized model parameter values obtained from the X-ray analysis, we then compared the modeled inverse Compton (IC) radiation with the published H.E.S.S. γ-ray data. Results. The spectral index within the four annuli increases with growing distance to the pulsar, whereas the surface brightness drops. With the adopted model we are able to reproduce the characteristics of the X-ray spectra. The model results for the VHE γ radiation, however, strongly deviate from the H.E.S.S. data.