We derive expressions for the local ideal magnetohydrodynamic (MHD) equations for awarped astrophysical disc using a warped shearing box formalism. A perturbation expansion of these equations to first order in the warping amplitude leads to a linear theory for the internal local structure of magnetized warped discs in the absence of magnetorotational instability (MRI) turbulence. In the special case of an external magnetic field oriented normal to the disc surface, these equations are solved semi-analytically via a spectral method. The relatively rapid warp propagation of low-viscosity Keplerian hydrodynamic warped discs is diminished by the presence of a magnetic field. The magnetic tension adds a stiffness to the epicyclic oscillations, detuning the natural frequency from the orbital frequency and thereby removing the resonant forcing of epicyclic modes characteristic of hydrodynamic warped discs. In contrast to a single hydrodynamic resonance, we find a series of Alfvénic-epicyclic modes which may be resonantly forced by the warped geometry at critical values of the orbital shear rate q and magnetic field strength. At these critical points large internal torques are generated and anomalously rapid warp propagation occurs. As our treatment omits MRI turbulence, these results are of greatest applicability to strongly magnetized discs.