Aharonov-Bohm conductance oscillations emerge as a result of gapless surface states in topological insulator nanowires. This quantum interference accompanies a change in the number of transverse one-dimensional modes in transport, and the density of states of such nanowires is also expected to show Aharonov-Bohm oscillations. Here, we demonstrate a novel characterization of topological phase in Bi2Se3 nanowire via nanomechanical resonance measurements. The nanowire is configured as an electromechanical resonator such that its mechanical vibration is associated with its quantum capacitance. In this way, the number of one-dimensional transverse modes is reflected in the resonant frequency, thereby revealing Aharonov-Bohm oscillations. Simultaneous measurements of DC conductance and mechanical resonant frequency shifts show the expected oscillations, and our model based on the gapless Dirac fermion with impurity scattering explains the observed quantum oscillations successfully. Our results suggest that the nanomechanical technique would be applicable to a variety of Dirac materials.