Effects of the Lorentz force on near-wall turbulence structures are investigated using the direct numerical simulation technique with the assumption of no induced magnetic field at low magnetic Reynolds number. A uniform magnetic field is applied in the streamwise (x), wall-normal (y) or spanwise (z) direction to turbulent flow in an infinitely long channel with non-conducting walls. The Lorentz force induced from the magnetic field suppresses the dynamically significant coherent structures near the wall. The skin friction decreases with increasing streamwise and spanwise magnetic fields, whereas it increases owing to the Hartmann effect when the strength of the wall-normal magnetic field exceeds a certain value. All the turbulence intensities and the Reynolds shear stress decrease with the wall-normal and spanwise magnetic fields, but the streamwise velocity fluctuations increase with the streamwise magnetic field although all other turbulence intensities decrease. It is also shown that the wall-normal magnetic field is much more effective than the streamwise and spanwise magnetic fields in reducing turbulent fluctuations and suppressing the near-wall streamwise vorticity, even though the wall-normal magnetic field interacts directly with the mean flow and results in drag increase at strong magnetic fields. In the channel with a strong streamwise magnetic field, two-dimensional streamwise velocity fluctuations u(y, z) exist, even after other components of the velocity fluctuations nearly vanish. In the cases of strong wall-normal and spanwise magnetic fields, all turbulence intensities, the Reynolds shear stress and vorticity fluctuations decrease rapidly and become zero. The turbulence structures are markedly elongated in the direction of the applied magnetic field when it is strong enough. It is shown that this elongation of the structures is associated with a rapid decrease of the Joule dissipation in time.