The neutron capture cross section of ⁵³Mn was measured with cold and reactor neutrons by the activation method, relative to the well-known cross section of ⁵⁹Co. Three targets containing a total of ≈10¹⁸ atoms ⁵³Mn in the form of chloride salt were prepared using a stock solution obtained from activated accelerator waste in the course of the ERAWAST initiative at Paul Scherrer Institute, Switzerland (PSI). Natural cobalt salt was added to the sample material as an internal neutron flux monitor. The total numbers of ⁵³Mn and ⁵⁹Co atoms in the target were deduced via mass spectrometric measurements at PSI. Cold-neutron activation was carried out at the ICON beamline at PSI. Reactor activation was performed at the LVR-15 research reactor of Research Centre Řež in a well-moderated neutron field of an outer reactor channel. The thermal-neutron capture cross section and the resonance integral were determined by the cadmium ratio method. The induced activities of ⁵⁴Mn and ⁶⁰Co were quantified by high-resolution γ-ray spectrometry. The obtained thermal-neutron capture cross section of 76.5 ± 1.4 b agrees well with previously reported results. The uncertainty of this value could be reduced by almost an order of magnitude with respect to older measurements and is on a level comparable to stable nuclides. The resonance integral of 43.1 ± 1.2 b was obtained for the real reactor spectrum with epithermal-spectrum shape factor α = 0.025.