Progressive telomere attrition or deficiency of the protective shelterin complex elicits a DNA damage response as a result of a cell's inability to distinguish dysfunctional telomeric ends from DNA double‐strand breaks. SNMIB/Apollo is a shelterin‐associated protein and a member of the SMN1/PSO2 nuclease family that localizes to telomeres through its interaction with TRF2. Here, we generated SNMIB/Apollo knockout mouse embryo fibroblasts (MEFs) to probe the function of SNMIB/Apollo at mammalian telomeres. SNMIB/Apollo null MEFs exhibit an increased incidence of G2 chromatid‐type fusions involving telomeres created by leading‐strand DNA synthesis, reflective of a failure to protect these telomeres after DNA replication. Mutations within SNMIB/Apollo's conserved nuclease domain failed to suppress this phenotype, suggesting that its nuclease activity is required to protect leading‐strand telomeres. SNMIB/Apollo^−/−ATM^−/− MEFs display robust telomere fusions when Trf2 is depleted, indicating that ATM is dispensable for repair of uncapped telomeres in this setting. Our data implicate the 5′–3′ exonuclease function of SNM1B/Apollo in the generation of 3′ single‐stranded overhangs at newly replicated leading‐strand telomeres to protect them from engaging the non‐homologous end‐joining pathway.