We present synchrotron x-ray diffraction, neutron powder diffraction, and time-of-flight inelastic neutron scattering measurements on the rare earth pyrochlore oxide Nd₂Zr₂O₇ to study the ordered state magnetic structure and cystal-field states. The structural characterization by high-resolution synchrotron x-ray diffraction confirms that the pyrochlore structure has no detectable O vacancies or Nd/Zr site mixing. The neutron diffraction reveals long-range all-in/all-out antiferromagnetic order below T_N ≈ 0.4 K with propagation vector k = (0 0 0) and an ordered moment of 1.26(2)μ_B/Nd at 0.1 K. The ordered moment is much smaller than the estimated moment of 2.65μ_B/Nd for the local ⟨111⟩ Ising ground state of Nd³⁺ (J = 9/2) suggesting that the ordering is partially suppressed by quantum fluctuations. The inelastic neutron scattering experiment further confirms the Ising anisotropic ground state of Nd³⁺ and also reveals its dipolar-octupolar character which possibly induces the quantum fluctuation. The crystal-field level scheme and ground state wave function have been determined.