Mutants in the actin nucleators Cappuccino and Spire disrupt the polarized microtubule network in the Drosophila oocyte that defines the anterior-posterior axis, suggesting that microtubule organization depends on actin. Here, we show that Cappuccino and Spire organize an isotropic mesh of actin filaments in the oocyte cytoplasm. capu and spire mutants lack this mesh, whereas overexpressed truncated Cappuccino stabilizes the mesh in the presence of Latrunculin A and partially rescues spire mutants. Spire overexpression cannot rescue capu mutants, but prevents actin mesh disassembly at stage 10B and blocks late cytoplasmic streaming. We also show that the actin mesh regulates microtubules indirectly, by inhibiting kinesin-dependent cytoplasmic flows. Thus, the Capu pathway controls alternative states of the oocyte cytoplasm: when active, it assembles an actin mesh that suppresses kinesin motility to maintain a polarized microtubule cytoskeleton. When inactive, unrestrained kinesin movement generates flows that wash microtubules to the cortex.