Protein aggregation in various cellular compartments is a hallmark of proteostasis impairment linked to aging and numerous pathologies. Mitochondrial function depends on a balanced interplay of proteins imported from the cytosol as well as those synthesized on mitochondrial ribosomes (mitoribosomes). Here, we reveal an unexpected susceptibility of mitoribosome biogenesis to organellar proteostatic stress. Importing aggregation-prone proteins into yeast and human mitochondria triggered a chain of detrimental events involving extensive co-aggregation of newly-imported mitoribosome subunits and other RNA-binding proteins, as well as local disruption of mitochondrial cristae morphology. As a result, mitoribosome assembly and mitochondrial translation were severely impaired, leading to respiratory deficiency and, ultimately, loss of mitochondrial DNA. Surprisingly, dysfunction of mitochondrial HSP60 phenocopied the ribosome biogenesis defect and inhibition of translation, indicating a pronounced chaperone dependence of mitoribosome proteins. Declining mitochondrial translation likely contributes to aging and diseases associated with deficiencies in mitochondrial protein quality control machinery.