Stem cells in many systems, including Drosophila germline stem cells (GSCs), increase ribosome biogenesis and translation during terminal differentiation. Here, we show that the H/ACA small nuclear ribonucleoprotein (snRNP) complex that promotes pseudouridylation of ribosomal RNA (rRNA) and ribosome biogenesis is required for oocyte specification. Reducing ribosome levels during differentiation decreased the translation of a subset of messenger RNAs that are enriched for CAG trinucleotide repeats and encode polyglutamine-containing proteins, including differentiation factors such as RNA-binding Fox protein 1. Moreover, ribosomes were enriched at CAG repeats within transcripts during oogenesis. Increasing target of rapamycin (TOR) activity to elevate ribosome levels in H/ACA snRNP complex-depleted germlines suppressed the GSC differentiation defects, whereas germlines treated with the TOR inhibitor rapamycin had reduced levels of polyglutamine-containing proteins. Thus, ribosome biogenesis and ribosome levels can control stem cell differentiation via selective translation of CAG repeat-containing transcripts.