Photoneutron cross sections were measured for 91Zr, 92Zr, and 94Zr near the neutron separation energy with quasimonochromatic gamma rays. The data exhibit some extra components around the neutron threshold. A coherent analysis of the photoneutron data for 92Zr together with the neutron capture on 91Zr based on the microscopic Hartree-Fock-Bogoliubov plus quasiparticle random-phase approximation model for the E1 strength has revealed the presence of an M1 resonance at 9 MeV. The microscopic approach systematically shows the same M1 strength in the photoneutron cross section for 91Zr and 94Zr. The total M1 strength is about 75% larger than the strength predicted by the systematics, being qualitatively consistent with the giant M1 resonance observed in the inelastic proton scattering.