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We analyze KMT-2019-BLG-1339, a microlensing event with an obvious but incompletely resolved brief anomaly feature around the peak of the light curve. Although the origin of the anomaly is identified to be a companion to the lens with a low mass ratio $q$, the interpretation is subject to two different degeneracy types. The first type is the ambiguity in $ρ$, representing the angular source radius scaled to the angular radius of the Einstein ring, $θ_{\rm E}$, and the other is the $s\leftrightarrow s^{-1}$ degeneracy. The former type, `finite-source degeneracy', causes ambiguities in both $s$ and $q$, while the latter induces an ambiguity only in $s$. Here $s$ denotes the separation (in units of $θ_{\rm E}$) in projection between the lens components. We estimate that the lens components have masses $(M_1, M_2)\sim (0.27^{+0.36}_{-0.15}~M_\odot, 11^{+16}_{-7}~M_{\rm J})$ and $\sim (0.48^{+0.40}_{-0.28}~M_\odot, 1.3^{+1.1}_{-0.7}~M_{\rm J})$ according to the two solutions subject to the finite-source degeneracy, indicating that the lens comprises an M dwarf and a companion with a mass around the planet/brown dwarf boundary or a Jovian-mass planet. It is possible to lift the finite-source degeneracy by conducting future observations utilizing a high resolution instrument because the relative lens-source proper motion predicted by the solutions are widely different.