We study the gauge covariance of the fermion propagator in Maxwell–Chern– Simons planar quantum electrodynamics (QED3 ) considering four-component spinors with parity-even and parity-odd mass terms for both fermions and photons. Starting with its tree-level expression in the Landau gauge, we derive a non-perturbative expression for this propagator in an arbitrary covariant gauge by means of its Landau–Khalatnikov–Fradkin transformation (LKFT). We compare our findings in the weak coupling regime with the direct one-loop calculation of the two-point Green function and observe perfect agreement up to a gauge-independent term. We also reproduce results derived in earlier works as special cases of our findings.