High-energy neutral solar radiation in the form of γ-rays and neutrons is produced as secondary products in solar flares. The characteristics of this emission can provide key information regarding the energization of charged particles, particularly when primary particles remain trapped in the corona. The Integrated Science Investigation of the Sun (IS⊙IS) suite on Parker Solar Probe is composed of instruments primarily intended to measure energetic charged particles. However, the High Energy Telescope (HET) in IS⊙IS was also designed with a supplementary neutral mode intended to measure γ-rays and neutrons. HET observed its first clear solar γ-ray event in connection with a hard X-ray flare, the eruption of a coronal mass ejection, and a solar energetic particle event on 2022 September 5. The X-ray spectral shape was observed to harden over the course of the event, culminating with the observation of γ-rays by HET. A coincident enhancement in the lower-energy Energetic Particle Instrument (EPI-Lo) was also observed, likely produced by incident solar γ-rays despite the EPI-Lo instrument not having any special neutral measurement capabilities. We use Monte Carlo modeling to reconstruct the incident γ-ray spectrum based on the measured spectrum to demonstrate that the combination of IS⊙IS instruments can measure hard X-rays and γ-rays from ∼60 keV–7 MeV. Despite the fact that this is a supplemental science goal of the mission, the capability of the IS⊙IS instruments to measure γ-rays is important for the study of this population due to the very limited instruments currently observing the Sun in γ-rays.