Small-scale anisotropic intermittency is examined in three-dimensional incompressible magnetohydrodynamic turbulence subjected to a uniformly imposed magnetic field. Orthonormal wavelet analyses are applied to direct numerical simulation data at moderate Reynolds number and for different interaction parameters. The magnetic Reynolds number is sufficiently low such that the quasistatic approximation can be applied. Scale-dependent statistical measures are introduced to quantify anisotropy in terms of the flow components, either parallel or perpendicular to the imposed magnetic field, and in terms of the different directions. Moreover, the flow intermittency is shown to increase with increasing values of the interaction parameter, which is reflected in strongly growing flatness values when the scale decreases. The scale-dependent anisotropy of energy is found to be independent of scale for all considered values of the interaction parameter. The strength of the imposed magnetic field does amplify the anisotropy of the flow.