The recent Zika virus (ZIKV) epidemic is associated with microcephaly in newborns. Although the connection between ZIKV and neurodevelopmental defects is widely recognized, the underlying mechanisms are poorly understood. Here we show that two recently isolated strains of ZIKV, an American strain from an infected fetal brain (FB-GWUH-2016) and a closely-related Asian strain (H/PF/2013), productively infect human iPSC-derived brain organoids. Both of these strains readily target to and replicate in proliferating ventricular zone (VZ) apical progenitors. The main phenotypic effect was premature differentiation of neural progenitors associated with centrosome perturbation, even during early stages of infection, leading to progenitor depletion, disruption of the VZ, impaired neurogenesis, and cortical thinning. The infection pattern and cellular outcome differ from those seen with the extensively passaged ZIKV strain MR766. The structural changes we see after infection with these more recently isolated viral strains closely resemble those seen in ZIKV-associated microcephaly.