Recent hypotheses propose that the human placenta and chorioamniotic membranes (CAMs) experience telomere length (TL)-mediated senescence. These hypotheses are based on mean TL (mTL) measurements, but replicative senescence is triggered by short and dysfunctional telomeres, not mTL. We measured short telomeres by a vanguard method, the Telomere shortest length assay, and telomere-dysfunction-induced DNA damage foci (TIF) in placentas and CAMs between 18-week gestation and at full-term. Both the placenta and CAMs showed a buildup of short telomeres and TIFs, but not shortening of mTL from 18-weeks to full-term. In the placenta, TIFs correlated with short telomeres but not mTL. CAMs of preterm birth pregnancies with intra-amniotic infection showed shorter mTL and increased proportions of short telomeres. We conclude that the placenta and probably the CAMs undergo TL-mediated replicative aging. Further research is warranted whether TL-mediated replicative aging plays a role in all preterm births.