Milk flavor varies greatly due to oxidative stress during storage. Several studies have documented the use of volatile biomarkers for determining milk oxidation, but only a few have focused on the development of inline procedures enabling the monitoring of milk oxidative stress. In this work, oxidative stress was induced in pasteurized milk samples by spiking increasing concentrations of copper ions (from 0 to 32 mg·L−1). During storage (4°C), hexanal evolution was monitored by a proton transfer reaction mass spectrometer. The mass fragment m/z 83 was selected as a biomarker for hexanal determination. Its intensity evolved with a sigmoidal trend, showing a maximum rate proportional to the Cu2+ content in milk. The proposed approach is simple, fast (up to 120 sample/h), sensitive (8.8 μg·m−3 per μM hexanal in the sample), with low limit of detection (0.5 μM, determined as 3 times the standard deviation divided by the slope of a calibration line), precise (<6%), with good recovery (99–104%), and noninvasive. The method can be used for laboratory screening of milk susceptibility toward oxidation or for quality control in the processing line.