SN 2001el is the first normal Type Ia supernova to show a strong, intrinsic polarization signal. In addition, during the epochs prior to maximum light, the Ca II IR triplet absorption is seen distinctly and separately at both normal photospheric velocities and at very high velocities. The high-velocity triplet absorption is highly polarized, with a different polarization angle than the rest of the spectrum. The unique observation allows us to construct a relatively detailed picture of the layered geometrical structure of the supernova ejecta: in our interpretation, the ejecta layers near the photosphere (ν ≈ 10, 000 km s-1) obey a nearly axial symmetry, while a detached, high-velocity structure (ν ≈ 18, 000-25, 000 km s-1) with high Ca II line opacity deviates from the photospheric axisymmetry. By partially obscuring the underlying photosphere, the high-velocity structure causes a more incomplete cancellation of the polarization of the photospheric light and so gives rise to the polarization peak and rotated polarization angle of the high-velocity IR triplet feature. In an effort to constrain the ejecta geometry, we develop a technique for calculating three-dimensional synthetic polarization spectra and use it to generate polarization profiles for several parameterized configurations. In particular, we examine the case in which the inner ejecta layers are ellipsoidal and the outer, high-velocity structure is one of four possibilities: a spherical shell, an ellipsoidal shell, a clumped shell, or a toroid. The synthetic spectra rule out the spherical shell model, disfavor a toroid, and find a best fit with the clumped shell. We show further that different geometries can be more clearly discriminated if observations are obtained from several different lines of sight. Thus, assuming that the high-velocity structure observed for SN 2001el is a consistent feature of at least a known subset of Type Ia supernovae, future observations and analyses such as these may allow one to put strong constraints on the ejecta geometry and hence on supernova progenitors and explosion mechanisms.