We report the discovery of a rare Mg IIλλ2796, 2803 doublet emission halo around a star-forming galaxy with log(M_⋆/M_⊙) = 10.3 ± 0.3 at z = 0.737 in deep (9.94 h) VLT/MUSE data from the MUSE-HUDF mosaic. While the central region prominently displays an absorption-dominated Mg II doublet characterized by discernible P-Cyg features, our examination reveals a remarkably extended Mg II emission spanning approximately ∼30 kpc from the central galaxy. We introduce a simple outflow radiative transfer modeling scheme based on the Sobolev approximation, and we employed a Bayesian Monte Carlo Markov chain fitting to find the best-fitting parameters that match our data. The model reproduces several key features of the observed Mg II halo and allowed us to constrain the kinematics and geometry of the outflowing gas. Our data are consistent with a biconical wind whose velocity increases with radius, pointing nearly toward the observer, with an opening angle of 59 ± 4°. In general, we find that our outflow model performs better in the inner regions of the galactic wind (≲10 kpc ≈6 half-light radii), reaching a velocity of ∼120 km s^‑1 at 10 kpc from the central galaxy. However, discrepancies between the data and the model in the outer regions suggest the possible influence of additional mechanisms, such as inflows, satellite interactions, or turbulence, which might significantly shape the circumgalactic medium (CGM) of galaxies at larger impact parameters. This analysis underscores the complexity of galactic outflows and encourages further exploration of the processes governing the dynamics of galactic winds through spatially resolved studies of the CGM.