Magnesium diboride (MgB2) superconducting wires have demonstrated commercial potential to replace niobium-titanium (NbTi) in terms of comparable critical current density. Its higher critical temperature makes MgB2 wire suitable for liquid-helium-free operation. We recently reported boron-11 isotope-based low-activation Mg11B2 superconducting wire with decent critical current density appropriate for low-cost superconducting fusion magnets. In this study, we have mainly focused on the neutron diffraction technique to measure the residual stress in Mg11B2 superconducting wire for the first time. The residual stress state was given qualitative and quantitative interpretation in terms of micro- and macrostress generation mechanisms based on the isotropic model confirmed by neutron texture measurements. The relationship between the stress/strain state in the wire and the transport critical current density is also discussed. This investigation could pave the way to further enhancement of the critical current density of low-activation Mg11B2 superconducting wires suitable for next-generation fusion grade magnets.