An extra Abelian gauge group arises naturally in a variety of extensions of the standard model. If the extra gauge boson, hidden photon, satisfies some conditions, then it can solve the muon g-2 anomaly, a persistent discrepancy between measured value and the standard model prediction of the anomalous magnetic moment of the muon. We investigate constraints on the hidden photon from precision measurements like electron g-2 and hydrogen spectroscopy, and show that the hidden photon which solves the muon g-2 anomaly can be examined by a experiment planed to start in the near future.