We explore the possibility that the ultracompact object XTE J1814-338 is a dark matter-admixed neutron star (DNS) based on a general-relativistic two-fluid approach, in which one fluid describes ordinary nuclear matter and the other dark matter. The equations of state of nuclear matter and dark matter are described by the Brueckner-Hartree-Fock (BHF) theory with realistic three-body forces and a generic bosonic self-interacting dark matter model, respectively. Based on the observational data, we determine the parameter space for XTE J1814-338 as a DNS, and find that only a halo stellar configuration with a high dark matter fraction is allowed. Furthermore, we predict other observable properties of XTE J1814-338 and provide robust lower bounds for these quantities.