The thermal neutron absorption cross section for the ⁵⁵Mn(n,γ)⁵⁶Mn reaction was measured at 0.0334 eV neutron energy relative to the flux monitor reaction ¹⁹⁷Au(n,g)¹⁹⁸Au using the TRIGA MARK-II research reactor in Bangladesh Atomic Energy Commission(BAEC), Savar, Dhaka, Bangladesh. The pure MnO₂ target sandwiched with two pure gold foils were irradiated by the unidirectional mono-energetic neutron beam in SAND (Savar Neutron Powder Diffractometer) coming through the Radial Beam Port-II of BAEC TRIGA reactor. The monitor reaction induced in a high purity gold foil is used to determine the effective neutron beam intensity. The activity induced in the sample and monitor foils were measured nondestructively by a high resolution HPGe detector (Canberra, 25% relative efficiency, 1.85 keV resolution at 1332 keV of ⁶⁰Co) coupled with the digital gamma spectrometer DSpec Jr^Tm (ORTEC) and Maestro-32 acquisition software. Corrections for gamma attenuation, neutron self-absorption, peak detection efficiency, etc. were implemented for cross section calculation. The cross section at this energy was found to be 11.28±0.56 barn which was 2.50% lower than the recently reported evaluated values of both ENDF/B-VII and JENDL-4 and 3.51% lower than that of ROSFOND-2010. The deviations in both cases were within estimated uncertainty quoted with the present experimental value. An extensive survey of literature reveals that the present experimental cross section value for ⁵⁵Mn(n,γ)⁵⁶Mn reaction at 0.0334 eV is determined for the first time.