In this study, a method that aims at detecting small and faint objects in noisy hyperspectral astrophysical images is presented. The particularity of the hyperspectral images that we are interested in is the high dynamics between object intensities. Detection of the smallest and faintest objects is challenging, because their signal-to-noise ratio is low, and if the brightest objects are not well reconstructed, their residuals can be more energetic than faint objects. This paper proposes a marked point process within a nonparametric Bayesian framework for the detection of galaxies in hyperspectral data. The efficiency of the method is demonstrated on synthetic images, and it provides good results for very faint objects in quasi-real astrophysical hyperspectral data.