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Cancer is a complex disease associated with abnormal DNA mutations. Not all tumors are cancerous and not all cancers are the same. Correct cancer type diagnosis can indicate the most effective drug therapy and increase survival rate. At the molecular level, it has been shown that cancer type classification can be carried out from the analysis of somatic point mutation. However, the high dimensionality and sparsity of genomic mutation data, coupled with its small sample size has been a hindrance in accurate classification of cancer. We address these problems by introducing a novel classification method called mClass that accounts for the sparsity of the data. mClass is a feature selection method that ranks genes based on their similarity across samples and employs their normalized mutual information to determine the set of genes that provide optimal classification accuracy. Experimental results on TCGA datasets show that mClass significantly improves testing accuracy compared to DeepGene, which is the state-of-the-art in cancer-type classification based on somatic mutation data. In addition, when compared with other cancer gene prediction tools, the set of genes selected by mClass contains the highest number of genes in top 100 genes listed in the Cancer Gene Census. mClass is available at https://github.com/mdahasan/mClass.