Whole genome prediction of complex phenotypic traits using high-density genotyping arrays has attracted a lot of attention, as it is relevant to the fields of plant and animal breeding and genetic epidemiology. Since the number of genotypes is generally much bigger than the number of samples, predictive models suffer from the <i>curse of dimensionality</i>. The curse of dimensionality problem not only affects the computational efficiency of a particular genomic selection method, but can also lead to a poor performance, mainly due to possible overfitting, or un-informative features. In this work, we propose a novel transductive feature selection method, called MINT, which is based on the MRMR (Max-Relevance and Min-Redundancy) criterion. We apply MINT on genetic trait prediction problems and show that, in general, MINT is a better feature selection method than the state-of-the-art inductive method MRMR.