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Context. Manganese is predominantly synthesised in Type Ia supernova (SN Ia) explosions. Owing to the entropy dependence of the Mn yield in explosive thermonuclear burning, SNe Ia involving near Chandrasekhar-mass (MCh) white dwarfs (WDs) are predicted to produce Mn-to-Fe ratios that significantly exceed those of SN Ia explosions involving sub-Chandrasekhar mass primary WDs. Of all current supernova explosion models, only SN Ia models involving near-MCh WDs produce [Mn/Fe] ≳ 0.0. Aims. Using the specific yields for competing SN Ia scenarios, we aim to constrain the relative fractions of exploding near-MCh to sub-MCh primary WDs in the Galaxy. Methods. We extract the Mn yields from three-dimensional thermonuclear supernova simulations that refer to different initial setups and progenitor channels. We then compute the chemical evolution of Mn in the solar neighborhood, assuming SNe Ia are made up of different relative fractions of the considered explosion models. Results. We find that due to the entropy dependence of freeze-out yields from nuclear statistical equilibrium, [Mn/Fe] depends strongly on the mass of the exploding WD, with near-MCh WDs producing substantially higher [Mn/Fe] than sub-MCh WDs. Of all nucleosynthetic sources potentially influencing the chemical evolution of Mn, only explosion models involving the thermonuclear incineration of near-MCh WDs predict solar or super-solar [Mn/Fe]. Consequently, we find in our chemical evolution calculations that the observed [Mn/Fe] in the solar neighborhood at [Fe/H] ≳ 0.0 cannot be reproduced without near-MCh SN Ia primaries. Assuming that 50% of all SNe Ia stem from explosive thermonuclear burning in near-MCh WDs results in a good match to data.