We demonstrate that the inherent nonlinearity of a microstructured optical fiber (MOF) may be used to achieve label-free selective biosensing, thereby eliminating the need for post-processing of the fiber. This first nonlinear biosensor utilizes a change in the modulational instability (MI) gain spectrum (a shift of the Stokes- or anti-Stokes wavelength) caused by the selective capture of biomolecules by a sensor layer immobilised on the walls of the holes in the fiber. We find that such changes in the MI gain spectrum can be made detectable, and that engineering of the dispersion is important for optimizing the sensitivity. The nonlinear sensor shows a sensitivity of around 10.4 nm/nm, defined as the shift in resonance wavelength per nm biolayer, which is a factor of 7.5 higher than the hitherto only demonstrated label-free MOF biosensor.