Axions were originally proposed to explain the strong-CP problem in QCD. Through axion-photon coupling, the Sun could be a major source of axions, which could be measured in solid state detection experiments with enhancements due to coherent Primakoff-Bragg scattering. The Majorana Demonstrator experiment has searched for solar axions with a set of ^{76}Ge-enriched high purity germanium detectors using a 33 kg-yr exposure collected between January, 2017 and November, 2019. A temporal-energy analysis gives a new limit on the axion-photon coupling as g_{aγ}<1.45×10^{-9} GeV^{-1} (95% confidence level) for axions with mass up to 100 eV/c^{2}. This improves laboratory-based limits between about 1 eV/c^{2} and 100 eV/c^{2}.