We present an analytical study on the spinmotive force (SMF) generated by translational motion of magnetic skyrmion. A SMF refers to an electrical voltage induced by dynamical magnetic textures, which reflects the spatiotemporal variation of the magnetization. The dynamics of a skyrmion thus can be detected by a SMF measurement, which may play an important role in future skyrmion-based technologies. We find the dependence of the SMF on skyrmion structure (e.g., skyrmion or anti-skyrmion, N\'{e}el or Bloch type, and the polarity of the skyrmion core) and Rashba and Dresselhaus spin-orbit couplings (SOCs). To this end, we derive explicit formulae for the spin-dependent electric fields originating from the two SOCs. Our findings offer a comprehensive understanding of the phenomenon and an estimation of the electrical voltage signal associated with a moving skyrmion for a given experiment.