Background: Several genetic markers have been associated with multiple sclerosis (MS) susceptibility; however, uncovering the genetic aetiology of the complex phenotypic expression of MS has been more difficult so far. The most common approach in imaging genetics is based on mass-univariate linear modelling (MULM), which faces several limitations. Objective: Here we apply a novel multivariate statistical model, sparse reduced-rank regression (sRRR), to identify possible associations of glutamate related single nucleotide polymorphisms (SNPs) and multiple MRI-derived phenotypes in MS. Methods: Seven phenotypes related to brain and lesion volumes for a total number of 326 relapsing–remitting and secondary-progressive MS patients and a total of 3809 glutamate related and control SNPs were analysed with sRRR, which resulted in a ranking of SNPs in decreasing order of importance (‘selection probability’). Lasso regression and MULM were used as comparative statistical techniques to assess consistency of the most important associations over different statistical models. Results: Five SNPs within the NMDA-receptor-2A-subunit (GRIN2A) domain were identified by sRRR in association with normalized brain volume (NBV), normalized grey matter volume and normalized white matter volume (NMWM). The association between GRIN2A and both NBV and NWMV was confirmed in MULM and Lasso analysis. Conclusions: Using a novel, multivariate regression model confirmed by two other statistical approaches we show associations between GRIN2A SNPs and phenotypic variation in NBV and NWMV in this first exploratory study. Replications in independent datasets are now necessary to validate these findings.