Zika virus (ZIKV) became a global health concern in 2016 due to its links to congenital microcephaly and other birth defects. Flaviviruses, including ZIKV, reorganize the endoplasmic reticulum (ER) to form a viroplasm, a compartment where virus particles are assembled. Microtubules (MTs) and microtubule-organizing centers (MTOCs) coordinate structural and trafficking functions in the cell, and MTs also support replication of flaviviruses. Here we investigated the roles of MTs and the cell’s MTOCs on ZIKV viroplasm organization and virus production. We show that a toroidal-shaped viroplasm forms upon ZIKV infection, and MTs are organized at the viroplasm core and surrounding the viroplasm. We show that MTs are necessary for viroplasm organization and impact infectious virus production. In addition, the centrosome and the Golgi MTOC are closely associated with the viroplasm, and the centrosome coordinates the organization of the ZIKV viroplasm toroidal structure. Surprisingly, viroplasm formation and virus production are not significantly impaired when infected cells have no centrosomes and impaired Golgi MTOC, and we show that MTs are anchored to the viroplasm surface in these cells. We propose that the viroplasm is a site of MT organization, and the MTs organized at the viroplasm are sufficient for efficient virus production.