Melting from a horizontal solid surface in the shape of a disk rotating about a vertical axis in the presence of a uniform transverse magnetic field is analyzed. The flow is governed by a dimensionless magnetic parameter M and another dimensionless parameter α representing the relative importance of melt rate and rotation times the viscosity. Similarity solutions of the nonlinear MHD equations are obtained by perturbations for small α and numerical integration for arbitrary α. A novel result of the analysis is that for M=1, two different solutions exist in a small α-range (0.170≤αs=0.174 and this αs decreases with the increase in M. Further the melt rate for which steady state solution exists decreases with increasing M. However, the magnetic field seems to effectively control the total film thickness. Torque required for the rotation as well as heat transfer rates at the boundaries are found for variations in α, M and the Prandtl number Pr.