In this paper we analyze an exactly solvable model consisting of an inertial Unruh-DeWitt detector which interacts linearly with a massless quantum field in Minkowski spacetime with a perfectly reflecting flat plane boundary. Firstly a set of coupled equations for the detector s and the field s Heisenberg operators are derived. Then we introduce the linear entropy as a measure of entanglement between the detector and the quantum field under mirror reflection, and solve the early-time detector-field entanglement dynamics. After coarse-graining the field, the dynamics of the detector s internal degree of freedom is described by a quantum Langevin equation, where the dissipation and noise kernels respectively correspond to the retarded Green s functions and Hadamard elementary functions of the free quantum field in a half space. At late times when the combined system is in a stationary state, we obtain exact expressions for the detector s covariance matrix and show that the detector-field entanglement decreases for smaller separation between the detector and the mirror. We explain the behavior of detector-field entanglement qualitatively with the help of a detector s mirror image, compare them with the case of two real detectors and explain the differences.