Although mechanisms of telomere protection are well-defined in differentiated cells, how stem cells sense and respond to telomere dysfunction, in particular telomeric double-strand breaks (DSBs), is poorly characterized. Here, we report the DNA damage signaling, cell cycle, and transcriptome changes in human induced pluripotent stem cells (iPSCs) in response to telomere-internal DSBs. We engineer human iPSCs with an inducible TRF1-FokI fusion protein to acutely induce DSBs at telomeres. Using this model, we demonstrate that TRF1-FokI DSBs activate an ATR-dependent DNA damage response, which leads to p53-independent cell cycle arrest in G2. Using CRISPR-Cas9 to cripple the catalytic domain of telomerase reverse transcriptase, we show that telomerase is largely dispensable for survival and lengthening of TRF1-FokI-cleaved telomeres, which instead are effectively repaired by robust homologous recombination (HR). In contrast to HR-based telomere maintenance in mouse embryonic stem cells, where HR causes ZSCAN4-dependent extension of telomeres beyond their initial lengths, HR-based repair of telomeric breaks is sufficient to maintain iPSC telomeres at a normal length, which is compatible with sustained survival of the cells over several days of TRF1-FokI induction. Our findings suggest a previously unappreciated role for HR in telomere maintenance in telomerase-positive iPSCs and reveal distinct iPSC-specific responses to targeted telomeric DNA damage.