Marked point processes have received a great attention in the recent years, for their ability to extract objects in large data sets as those obtained in e.g. biological studies or hyperspectral remote sensing frameworks. This paper focuses on an original Bayesian point pro- cess estimation for the detection of galaxies from the hyperspectral MUSE data 'cube'. It is shown that this approach allows to obtain a a synthetic representation of the detection problem and circumvent the computational complexity inherent to high dimensional pixel based approaches. The reversible jump Monte Carlo Markov Chain (RJ- MCMC) implemented to sample the parameters is detailed, and the results obtained on benchmark data mimicking the real instrument are provided.