The Fuzzy C-Means (FCM) algorithm is a widely used and flexible approach to automated image segmentation, especially in the field of brain tissue segmentation from 3D MRI, where it addresses the problem of partial volume effects. In order to improve its robustness to classical image deterioration, namely noise and bias field artifacts, which arise in the MRI acquisition process, we propose to integrate into the FCM segmentation methodology concepts inspired by the Non-Local (NL) framework, initially defined and considered in the context of image restoration. The key algorithmic contributions of this article are the definition of an NL data term and an NL regularisation term to efficiently handle intensity inhomogeneities and noise in the data. The resulting new energy formulation is then built into an NL/FCM brain tissue segmentation algorithm. Experiments performed on both synthetic and real MRI data, leading to the classification of brain tissues into grey-matter, white matter and cerebrospinal fluid, indicate a significant improvement in performance in the case of higher noise levels, when compared to a range of standard algorithms.