The rapid and non-destructive detection of mechanical damage to fruit during postharvest supply chains is important for monitoring fruit deterioration in time and optimizing freshness preservation and packaging strategies. As fruit is usually packed during supply chain operations, it is difficult to detect whether it has suffered mechanical damage by visual observation and spectral imaging technologies. In this study, based on the volatile substances (VOCs) in yellow peaches, the electronic nose (e-nose) technology was applied to non-destructively predict the levels of compression damage in yellow peaches, discriminate the damaged fruit and predict the time after the damage. A comparison of the models, established based on the samples at different times after damage, was also carried out. The results show that, at 24 h after damage, the correct answer rate for identifying the damaged fruit was 93.33%, and the residual predictive deviation in predicting the levels of compression damage and the time after the damage, was 2.139 and 2.114, respectively. The results of e-nose and gas chromatography-mass spectrophotometry (GC–MS) showed that the VOCs changed after being compressed—this was the basis of the e-nose detection. Therefore, the e-nose is a promising candidate for the detection of compression damage in yellow peach.