We show that the X-ray line flux of the Mn K α line at 5.9 keV from the decay of 55 Fe is a promising diagnostic to distinguish between Type Ia supernova (SN Ia) explosion models. Using radiation transport calculations, we compute the line flux for two three-dimensional explosion models: a near-Chandrasekhar mass delayed detonation and a violent merger of two (1.1 and 0.9 M ⊙ ) white dwarfs. Both models are based on solar metallicity zero-age main sequence progenitors. Due to explosive nuclear burning at higher density, the delayeddetonation model synthesises ∼3.5 times more radioactive 55 Fe than the merger model. As a result, we find that the peak Mn K α line flux of the delayed-detonation model exceeds that of the merger model by a factor of ∼4.5. Since in both models the 5.9 keV X-ray flux peaks five to six years after the explosion, a single measurement of the X-ray line emission at this time can place a constraint on the explosion physics that is complementary to those derived from earlier phase optical spectra or light curves. We perform detector simulations of current and future X-ray telescopes to investigate the possibilities of detecting the X-ray line at 5.9 keV. Of the currently existing telescopes, XMM-Newton/pn is the best instrument for close ( 1 − 2 Mpc), non-background limited SNe Ia because of its large effective area. Due to its low instrumental background, Chandra/ACIS is currently the best choice for SNe Ia at distances above ∼2 Mpc. For the delayed-detonation scenario, a line detection is feasible with Chandra up to ∼3 Mpc for an exposure time of 10 6 s. We find that it should be possible with currently existing X-ray instruments (with exposure times 5 × 10 5 s) to detect both of our models at sufficiently high S/N to distinguish between them for hypothetical events within the Local Group. The prospects for detection will be better with future missions. For example, the proposed Athena/X-IFU instrument could detect our delayed-detonation model out to a distance of ∼5 Mpc. This would make it possible to study future events occurring during its operational life at distances comparable to those of the recent supernovae SN 2011fe (∼6.4 Mpc) and SN 2014J (∼3.5 Mpc).