Recent results and data suggest that high magnetic fields in neutron stars (NS) strongly affect the characteristics (radius, mass) of the star. Such stars are even separated into a class known as magnetars, for which the surface magnetic field is greater than 1014 G. In this work we discuss the effect of such a high magnetic field on the phase transition of a NS to a quark star (QS). We study the effect of magnetic field on the transition from NS to QS including the magnetic-field effect in the equation of state (EoS). The inclusion of the magnetic field increases the range of baryon number densities for which the flow velocities of the matter in the respective phase are finite. The magnetic field helps in initiation of the conversion process. The velocity of the conversion front, however, decreases due to the presence of the magnetic field, as the presence of the magnetic field reduces the effective pressure (P). The magnetic field of the star is decreased by the conversion process, and the resultant QS has lower magnetic field than the initial NS.