Ultra-relativistic heavy-ion collisions create a hot and dense medium of deconfined quarks and gluons, the quark$-$gluon plasma (QGP), in which parton energy loss ("jet quenching") is a key probe of hot medium properties. While parton energy loss has been firmly established in large systems such as Pb$-$Pb and Au$-$Au collisions, no unambiguous direct evidence exists in smaller systems such as high-multiplicity p$-$Pb and pp collisions. To probe the onset of parton energy loss at intermediate system size, measurements of neutral-pion production are presented in this Letter for oxygen$-$oxygen (OO) and proton$-$oxygen (pO) collisions recorded with the ALICE detector in July 2025, relative to a pp baseline. The nuclear modification factor $R_{\rm OO}$ is suppressed relative to unity with a transverse-momentum dependence similar to that observed in Pb$-$Pb collisions, consistent with a previous CMS measurement in OO collisions with charged particles. As $R_{\rm OO}$ contains contributions from both cold and hot nuclear matter effects, $R_{\rm pO}$ is also presented in order to constrain cold nuclear matter (CNM) contributions. $R_{\rm pO}$ is found to be compatible with unity, indicating that CNM effects alone cannot account for the suppression observed in $R_{\rm OO}$. Final-state effects are isolated using the measured double ratio $R_{\rm OO} \left/ R_{\rm pO}^2 \right.$, which largely cancels CNM contributions and exhibits a significant suppression relative to expectations without energy loss at a $4.9σ$ level. Theoretical models incorporating parton energy loss via different mechanisms predict a significant suppression of the $R_{\rm OO} \left/ R_{\rm pO}^2 \right.$ relative to unity, consistent with the data. These findings establish parton energy loss in OO collisions, extending experimental evidence for jet quenching to the smallest nuclear system studied to date.