Message-specific translational regulation mechanisms shape the biogenesis of multimeric oxidative phosphorylation (OXPHOS) enzyme in mitochondria from the yeast Saccharomyces cerevisiae. These mechanisms, driven mainly by the action of mRNA-specific translational activators, help to coordinate synthesis of OXPHOS catalytic subunits by the mitoribosomes with both the import of their nucleus-encoded partners and their assembly to form the holocomplexes. However, little is known regarding the role that the mitoribosome itself may play in mRNA-specific translational regulation. Here, we show that the mitoribosome small subunit protein Cox24/mS38, known to be necessary for mitoribosome-specific intersubunit bridge formation and 15S rRNA H44 stabilization, is required for efficient mitoribogenesis. Consequently, mS38 is necessary to sustain the overall mitochondrial protein synthesis rate, despite an adaptive ∼2-fold increase in mitoribosome abundance in mS38-deleted cells. Additionally, the absence of mS38 preferentially disturbs translation initiation of COX1, COX2, and COX3 mRNAs, without affecting the levels of mRNA-specific translational activators. We propose that mS38 confers the mitochondrial ribosome an intrinsic capacity of translational regulation, probably acquired during evolution from bacterial ribosomes to facilitate the translation of mitochondrial mRNAs, which lack typical anti-Shine-Dalgarno sequences.