The reaction cross sections of 55Mn(n, γ)56Mn and 65Cu(n, γ)66Cu have been measured over a neutron energy range from 1 keV to 4 MeV. The racetrack microtron accelerator-based neutron source was used for the cross-section measurement, which generates a neutron spectrum from 1 keV to 4 MeV. Moreover, the cross-sections of the nuclear reaction were calculated using TALYS-1.2 and EMPIRE nuclear codes. It has been observed that the experimental cross sections of manganese and copper are 8.5 mb and 4.5 mb, respectively, and they are quite close to the TALYS, EMPIRE, and evaluated data of ENDF/B-VII.0, ENDF/B-VII.1, JEFF-3.1.2, and EXFOR. For (n, γ) reactions studied in the present work, the results obtained using TALYS and EMPIRE codes are in agreement with literature values when the radiative capture width Гγ and the width fluctuation parameter, respectively, functioned by being adjusted to a suitable value. Further, the deviation factor for measured and theoretical cross sections has also been determined and it is found to be better for the 55Mn(n, γ)56Mn reaction obtained using TALYS compared to EMPIRE.