The linear stability of two viscous electrically conducting quiescent fluids, separated by a plane interface, and permeated by a sheared magnetic field parallel to the interface is studied. An analytical study using a short-wavelength approximation shows that, in the absence of surface tension, if the magnetic field vanishes on the unperturbed interface, the configuration is always unstable provided the magnetic diffusivities of the two fluids are different. When the unperturbed magnetic field does not vanish on the interface it may stabilize or destabilize the configuration depending on the values of certain parameters. The growth rates for the instability obtained using a short-wavelength approximation are shown to be in good agreement with the results obtained by numerical solution. The numerical study further shows that the instability has maximum growth rate for wavenumbers of order unity and persists even for long-wavelength perturbations. A physical explanation for the instability is provided.