Detection of local strain at the nanometer scale with high sensitivity remains challenging. Here we report near-field infrared nano-imaging of local strains in bilayer graphene through probing strain-induced shifts of phonon frequency. As a non-polar crystal, intrinsic bilayer graphene possesses little infrared response at its transverse optical (TO) phonon frequency. The reported optical detection of local strain is enabled by applying a vertical electrical field that breaks the symmetry of the two graphene layers and introduces finite electrical dipole moment to graphene phonon. The activated phonon further interacts with continuum electronic transitions, and generates a strong Fano resonance. The resulted Fano resonance features a very sharp near-field infrared scattering peak, which leads to an extraordinary sensitivity of ~0.002% for the strain detection. Our studies demonstrate the first nano-scale near-field Fano resonance, provide a new way to probe local strains with high sensitivity in non-polar crystals, and open exciting possibilities for studying strain-induced rich phenomena.