Single-stranded DNA secondary structures such as G-quadruplexes (G4s) can potentially disrupt transcription, replication, and repair. Using bioinformatic analysis, here, we show that BMI1 is enriched at putative G4s flanked by heterochromatin domains and that BMI1 knockdown in human dermal fibroblasts (HDFs) resulted in heterochromatin relaxation and G4 induction, followed by replication stress and genomic instability. In these cells, G4s co-localized with large 53BP1 and PCNA foci resembling replication catastrophes. Inhibiting transcription partly attenuated DNA damage, suggesting rescue of transcription-replication collisions at difficult-to-replicate sequences. In BMI1 knockdown or pyridostatin-exposed HDFs, the Werner helicase accumulated and co-localized with G4s, and acute WRN knockdown resulted in G4 induction. In HDFs from Werner and Hutchinson-Gilford progeria syndromes, loss of heterochromatin and nuclear envelope anomalies were associated with G4 induction and DNA damage, and nuclear envelope anomalies were also prominent following BMI1 knockdown. These findings suggest that heterochromatin-mediated repression of G4s attenuates replication stress and genomic instability, and that this mechanism may be shared across distinct progeroid models.