The vast majority of recurrent somatic mutations arising in tumors affect protein-coding genes in the nuclear genome. Here, through population-scale analysis of 14,079 whole tumor genomes, we report the discovery of highly recurrent mutations affecting both the small (12S, MT-RNR1) and large (16S, MT-RNR2) RNA subunits of the mitochondrial ribosome. Compared to non-hotspot positions, mitochondrial rRNA hotspots preferentially affected positions participating in Watson-Crick base pairing and tended to arise at positions under strong purifying selection in the germline. Using precision mtDNA base editing, we engineered models of an exemplar MT-RNR1 hotspot mutation, m.1227G>A. Multimodal profiling revealed a heteroplasmy-dependent decrease in mitochondrial function and loss of respiratory chain subunits from a heteroplasmic dosage of ~10%, which were corroborated with single cell profiling of mtDNA heteroplasmy and gene expression. Mutation of evolutionarily conserved and germline constrained positions in ribosomal RNA that disrupt mitochondrial translation therefore represent a novel class of functionally dominant, pathogenic mtDNA mutations that are under positive selection in cancer genomes.