Lamin A/C is a major constituent of the nuclear lamina, a thin filamentous protein layer that lies beneath the nuclear envelope. Here we show that lamin A/C deficiency in mouse embryonic fibroblasts (Lmna-/- MEFs) diminishes the ability of these cells to polarize at the edge of a wound and significantly reduces cell migration speed into the wound. Moreover, lamin A/C deficiency induces significant separation of the microtubule organizing center (MTOC) from the nuclear envelope. Investigations using ballistic intracellular nanorheology reveal that lamin A/C deficiency also dramatically affects the micromechanical properties of the cytoplasm. Both the elasticity (stretchiness) and the viscosity (propensity of a material to flow) of the cytoplasm in Lmna-/- MEFs are significantly reduced. Disassembly of either the actin filament or microtubule networks in Lmna+/+ MEFs results in decrease of cytoplasmic elasticity and viscosity down to levels found in Lmna-/- MEFs. Together these results show that both the mechanical properties of the cytoskeleton and cytoskeleton-based processes, including cell motility, coupled MTOC and nucleus dynamics, and cell polarization, depend critically on the integrity of the nuclear lamina, which suggest the existence of a functional mechanical connection between the nucleus and the cytoskeleton. These results also suggest that cell polarization during cell migration requires tight mechanical coupling between MTOC and nucleus, which is mediated by lamin A/C.