The recent experimental observation of the quantum anomalous Hall effect(1-5) has cast significant attention on magnetic topological insulators. In these magnetic counterparts of conventional topological insulators such as Bi2Te3, a long-range ferromagnetic state can be established by chemical doping with transition-metal elements(6-8). However, a much richer electronic phase diagram can emerge and, in the specific case of Cr-doped Bi-2(SexTe1-x)(3), a magnetic quantum phase transition tuned by the actual chemical composition has been reported(8). From an application-oriented perspective, the relevance of these results hinges on the possibility to manipulate magnetism and electronic band topology by external perturbations such as an electric field generated by gate electrodes-similar to what has been achieved in conventional diluted magnetic semiconductors(9). Here, we investigate the magnetotransport properties of Cr-doped Bi-2(SexTe1-x)(3) with different compositions under the effect of a gate voltage. The electric field has a negligible effect on magnetic order for all investigated compositions, with the remarkable exception of the sample close to the topological quantum critical point, where the gate voltage reversibly drives a ferromagnetic-to-paramagnetic phase transition. Theoretical calculations show that a perpendicular electric field causes a shift in the electronic energy levels due to the Stark effect, which induces a topological quantum phase transition and, in turn, a magnetic phase transition.