Hyperspectral imaging (HSI) provides high-resolution recording of the spectral information at every spatial point (pixel) of an object throughout a contiguous range of wavelengths. This paper reports an attempt at exploring the application of HSI in transmittance mode for the identification and quantification of corrosion in transparent historical glass, which is difficult to identify by visual inspection. This was done using model glass samples mimicking historical composition and subjected to artificial ageing in the presence of volatile organic compounds. Hyperspectral images of unaged and aged glass samples were recorded with two cameras covering visible and near infrared (VNIR, 400–1000 nm) and short-wave infrared range (SWIR, 1000–2500 nm) using a custom-made HSI set-up in transmission mode. The HSI data were further processed to classify and visualize corrosion in different ageing environments and ageing periods. The results show that HSI can be employed as a valuable tool to assess glass corrosion at early stages, especially by analysing the SWIR spectral region—which shows the water absorption by the glass matrix due to corrosion.