A search of axions produced in nuclear transitions was performed at the Kuo-Sheng Nuclear Power Station with a high-purity germanium detector of mass 1.06 kg at a distance of 28 m from the 2.9 GW reactor core. The expected experimental signatures were monoenergetic lines produced by their Primakoff or Compton conversions at the detector. Based on 459.0/96.3 days of reactor ON/OFF data, no evidence of axion emissions were observed and constraints on the couplings g(a gamma gamma) and g(aee) versus axion mass m(a) within the framework of invisible axion models were placed. The KSVZ and DFSZ models can be excluded for 10(4) eV less than or similar to m(a)less than or similar to 10(6) eV. Model-independent constraints on g(a gamma gamma)center dot g(aNN)(1)< 7.7x10(-9) GeV-2 for m(a)less than or similar to 10(5) eV and g(aee)center dot g(aNN)(1)< 1.3x10(-10) for m(a)less than or similar to 10(6) eV at 90% confidence level were derived. This experimental approach provides a unique probe for axion mass at the keV-MeV range not accessible to the other techniques.