We demonstrate a nonlinear fiber-optic strain sensor, which uses the shifts of four-wave mixing Stokes and anti-Stokes peaks caused by the strain-induced changes in the structure and refractive index of a microstructured optical fiber. The sensor thus uses the inherent nonlinearity of the fiber and does not require any advanced postprocessing of the fiber. Strain sensitivity of -0.23 pm/με is achieved experimentally and numerical simulations reveal that for the present fiber the sensitivity can be increased to -4.46 pm/με by optimizing the pump wavelength and power.