Chromosomal instability (CIN) causes structural and numerical chromosome aberrations and represents a hallmark of cancer. Replication stress (RS) has emerged as a driver for structural chromosome aberrations while mitotic defects can cause whole chromosome missegregation and aneuploidy. Recently, first evidence indicated that RS can also influence chromosome segregation in cancer cells exhibiting CIN, but the underlying mechanisms remain unknown. Here, we show that chromosomally unstable cancer cells suffer from very mild RS, which allows efficient proliferation and which can be mimicked by treatment with very low concentrations of aphidicolin. Both, endogenous RS and aphidicolin-induced very mild RS cause chromosome missegregation during mitosis leading to the induction of aneuploidy. Moreover, RS triggers an increase in microtubule plus end growth rates in mitosis, an abnormality previously identified to cause chromosome missegregation in cancer cells. In fact, RS-induced chromosome missegregation is mediated by increased mitotic microtubule growth rates and is suppressed after restoration of proper microtubule growth rates and upon rescue of replication stress. Hence, very mild and cancer-relevant RS triggers aneuploidy by deregulating microtubule dynamics in mitosis.