By inverting the distributions of galaxies’ apparent ellipticities and misalignment angles (measured around the projected half-light radius R _e) between their photometric and kinematic axes, we study the intrinsic shape distribution of 189 slow rotator early-type galaxies with stellar masses 2 × 10¹¹ M _⊙ < M _* < 2 × 10¹² M _⊙, extracted from a sample of about 2200 galaxies with integral-field stellar kinematics from the data release 14 (DR14) of the fourth-generation Sloan Digital Sky Survey IV (SDSS-IV) Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) integral field unit (IFU) survey. Thanks to the large sample of slow rotators, Graham et al. showed that there is clear structure in the misalignment angle distribution, with two peaks at both 0° and 90° misalignment (characteristic of oblate and prolate rotation, respectively). Here we invert the observed distribution from Graham et al. The large sample allows us to go beyond the known fact that slow rotators are weakly triaxial and to place useful constraints on their intrinsic triaxiality distribution (around 1 R _e) for the first time. The shape inversion is generally non-unique. However, we find that, for a wide set of model assumptions, the observed distribution clearly requires a dominant triaxial-oblate population. For some of our models, the data suggest a minor triaxial-prolate population, but a dominant prolate population is ruled out.