Massive stars die an explosive death as a core-collapse supernova (CCSN). The exact physical processes that cause the collapsing star to rebound into an explosion are not well understood1–3, and the key to resolving this issue may lie in the measurement of the shape of CCSNe ejecta. Spectropolarimetry is the only way to perform this measurement for CCSNe outside the Milky Way and Magellanic Clouds. We present the infrared spectropolarimetric detection of a CCSN enabled by the new highly sensitive WIRC+Pol instrument at Palomar Observatory, which can observe CCSNe (magnitude M = −17 mag) out to 20 Mpc at ~0.1% polarimetric precision. Infrared spectropolarimetry is less affected than optical spectropolarimetry by dust scattering in the circumstellar and interstellar media, thereby providing a less biased probe of the intrinsic geometry of the supernova ejecta. SN 2018hna, a SN 1987A-like explosion, shows 2.0 ± 0.3% continuum polarization in the J band oriented at ~160° on sky 182 days after the explosion. Assuming a prolate geometry as in SN 1987A, we infer an ejecta axis ratio of <0.48 with the axis of symmetry pointing at a 70° position angle. The axis ratio is similar to that of SN 1987A, suggesting that the two CCSNe may share intrinsic geometry and inclination angles. Our data do not rule out oblate ejecta. We also observe one other CCSN and two thermonuclear supernovae in the J band. Supernova 2020oi, a stripped-envelope type Ic SN in Messier 100 has broadband p = 0.37 ± 0.09% at peak light, indicative of either a 10% asymmetry or host interstellar polarization. The type Ia SNe 2019ein and 2020ue have <0.33% and <1.08% polarization near peak light, indicative of asymmetries of less than 10% and 20%, respectively.