Anisotropies of the cosmic optical background (COB) and cosmic near-IR background (CNIRB) are capable of addressing some of the key questions in cosmology and astrophysics. In this work, we measure and analyze the angular power spectra of the simulated COB and CNIRB in the ultra-deep field of the China Space Station Telescope (CSST-UDF). The CSST-UDF covers about 9 square degrees, with magnitude limits ~28.3, 28.2, 27.6, 26.7 for point sources with 5-sigma detection in the r (0.620 um), i (0.760 um), z (0.915 um), and y (0.965 um) bands, respectively. According to the design parameters and scanning pattern of the CSST, we generate mock data, merge images and mask the bright sources in the four bands. We obtain four angular power spectra from l=200 to 2,000,000 (from arcsecond to degree), and fit them with a multi-component model including intrahalo light (IHL) using the Markov chain Monte Carlo (MCMC) method. We find that the signal-to-noise ratio (SNR) of the IHL is larger than 8 over the range of angular scales that are useful for astrophysical studies (l~10,000-400,000). Comparing to previous works, the constraints on the model parameters are improved by factors of 3~4 in this study, which indicates that the CSST-UDF survey can be a powerful probe on the cosmic optical and near-IR backgrounds.