This paper studies a robust algorithm allowing the estimation of the center and the radius of a hypersphere in the presence of outliers. To that extend, the Student-t distribution is assigned to the noise samples to mitigate the impact of the outliers. A von Mises-Fisher prior distribution is also assigned to latent variables in order to exploit the fact that the observed samples are located in a part of the hypersphere. A robust Bayesian algorithm based on a Gibbs sampler is then proposed to solve the hypersphere fitting problem. This algorithm generates samples asymptotically distributed according to the joint distribution of the unknown parameters of the hypersphere (radius and center), as well as the other model parameters such as the noise variance. Simulations conducted on synthetic data with controlled ground truth allow the performance of this algorithm to be appreciated.