Primary microcephaly is caused by the depletion of neuronal progenitor cells during brain development, resulting in reduced brain size and impaired cognitive abilities. It arises due to recessive loss-of-function mutations of cell division genes, that are thought to cause neuronal progenitor loss either because of aneuploidy-driven apoptosis, spindle orientation defects, or prolonged mitotic timing. Loss of the two most frequently impaired microcephaly genes, WDR62 and ASPM, elicits, however, none of these phenotypes in human cells. Instead, their loss slows down poleward microtubule flux and results in transient lagging chromosomes in anaphase. Whether these defects cause primary microcephaly is, however, unknown. Here we show that slower poleward microtubule flux rates lead to transient lagging anaphase chromosomes that elicit an Aurora-B dependent activation of 53BP1 and the p53-target p21, impairing cell proliferation. Co-depletion of CAMSAP1, an inhibitor of microtubule depolymerization at spindle poles, restores normal poleward flux rates, suppresses the lagging chromosomes, silences 53BP1 and p21 activation, and allows normal cell proliferation in WDR62-depleted cells. In Drosophila melanogaster larvae knock-down of the CAMSAP1 ortholog Patronin suppresses the small brain, the neuroblast depletion, and the impaired cognitive phenotype associated with WDR62 loss. We thus postulate that poleward microtubule flux defects in neuronal progenitor cells drive primary microcephaly due to the activation of 53BP1 and p21 in response to transient lagging chromosomes in anaphase. Since loss of most cell division genes associated with primary microcephaly can lead to such transient lagging chromosomes, we speculate that they might represent a common cause of this disease.