Auxin’s role in the post-ripening of peaches is widely recognized as important. However, little is known about the processes by which auxin regulates fruit post-ripening. As one of the early auxin-responsive genes, it is critical to understand the role of small auxin-up RNA (SAUR) genes in fruit post-ripening and softening. Herein, we identified 72 PpSAUR auxin-responsive factors in the peach genome and divided them into eight subfamilies based on phylogenetic analysis. Subsequently, the members related to peach post-ripening in the PpSAUR gene family were screened, and we targeted PpSAUR43. The expression of PpSAUR43 was decreased with fruit post-ripening in melting flesh (MF) fruit and was high in non-melting flesh (NMF) fruit. The overexpression of PpSAUR43 showed a slower rate of firmness decline, reduced ethylene production, and a delayed fruit post-ripening process. The MADS-box gene family plays an important regulatory role in fruit ripening. In this study, we showed with yeast two-hybrid (Y2H) and bimolecular fluorescence complementation (BIFC) experiments that PpSAUR43 can interact with the MADS-box transcription factor PpCMB1(PpMADS2), which indicates that PpSAUR43 may inhibit fruit ripening by suppressing the function of the PpCMB1 protein. Together, these results indicate that PpSAUR43 acts as a negative regulator involved in the peach post-ripening process.