Detailed spectropolarimetric studies may hold the key to probing the explosion mechanisms and the progenitor scenarios of Type Ia supernovae (SNeIa). We present multi-epoch spectropolarimetry and imaging polarimetry of SN2019ein, an SNIa showing high expansion velocities at early phases. The spectropolarimetry sequence spans from 11 to +10d relative to peak brightness in the B band. We find that the level of the continuum polarization of SN2019ein, after subtracting estimated interstellar polarization, is in the range 0.00.3percent, typical for SNeIa. The polarization position angle remains roughly constant before and after the SN light-curve peak, implying that the inner regions share the same axisymmetry as the outer layers. We observe high polarization (1 per cent) across both the Siii 6355 and Caii near-infrared triplet features. These two lines also display complex polarization modulations. The spectropolarimetric properties of SN2019ein rule out a significant departure from spherical symmetry of the ejecta for up to a month after the explosion. These observations disfavour merger-induced and double-detonation models for SN2019ein. The imaging polarimetry shows weak evidence for a modest increase in polarization after 20d since the B-band maximum. If this rise is real and is observed in other SNeIa at similar phases, we may have seen, for the first time, an aspherical interior similar to what has been previously observed for SNeIIP. Future polarization observations of SNeIa extending to post-peak epochs will help to examine the inner structure of the explosion.