Recently, Cd3As2 has attracted intensive research interest as an archetypical Dirac semimetal, hosting three dimensional linear-dispersive electronic bands near the Fermi level. Previous studies have shown that single-crystalline Cd3As2 has an anomalously low lattice thermal conductivity, ranging from 0.3 W/mK to 0.7 W/mK at 300 K, which has been attributed to point defects. In this work, we combine first-principles lattice dynamics calculations and temperature-dependent highresolution Raman spectroscopy of high-quality single-crystal thin films grown by molecular beam epitaxy to reveal the existence of a group of soft optical phonon modes at the Brillouin zone center of Cd3As2. These soft phonon modes significantly increase the scattering phase space of heatcarrying acoustic phonons and are the origin of the low lattice thermal conductivity of Cd3As2. Furthermore, we show that the interplay between the phonon-phonon Umklapp scattering rates and the soft optical phonon frequency explains the unusual non-monotonic temperature dependence of the lattice thermal conductivity of Cd3As2. Our results further suggest that the soft phonon modes are potentially induced by a Kohn anomaly associated with the Dirac nodes, in analogy to similar, nonetheless weaker, effects in graphene and Weyl semimetals.