Recent studies show that an intermediate mass black hole (IMBH) may develop a dark matter (DM) minihalo according to some BH formation scenarios. We consider a binary system composed of an IMBH surrounded by a DM minispike and a stellar mass object orbiting around the IMBH. The binary evolves due to gravitational pull and dynamical friction from the DM minispike and backreaction from its gravitational wave (GW) radiation which can be detected by future space-borne GW experiments such as eLISA/NGO. We consider a single power-law model for the DM minispike which is assumed to consist of nonannihilating DM particles and derive GW waveforms including the DM effects analytically. We demonstrate that a detection of GWs from such a binary with eLISA/NGO is affected by the DM effects and enables us to measure the DM minispike parameters accurately. For instance, in our reference case originally advocated by Zhao and Silk [Phys. Rev. Lett. 95, 011301 (2005)] and Bertone et al. [Phys. Rev. D 72, 103517 (2005)], we could determine the power-law index α of the DM minispike radial profile with a 1 σ relative error of ±5 ×1 0^-6 for a GW signal with signal-to-noise ratio 10 and assuming a five-year observation with eLISA. We also investigate how accurately the DM parameters can be determined for various values of the slope of the DM minispike and the masses of the IMBH-stellar mass object binary surrounded by the DM minispike. We find that the power-law index α is measurable at 10% level even for a slightly flatter radial distribution of α ∼1.7 . We clarify that the larger masses of the IMBH and the stellar object lead to the worse measurement accuracies of the DM parameters because the number of GW cycles becomes smaller.