Fatty acid composition and mineral nutrient concentrations can affect the nutritional and postharvest properties of fruit and so assessing the chemistry of fresh produce is important for guaranteeing consistent quality throughout the value chain. Current laboratory methods for assessing fruit quality are time-consuming and often destructive. Non-destructive technologies are emerging that predict fruit quality and can minimise postharvest losses, but it may be difficult to develop such technologies for fruit with thick skin. This study aimed to develop laboratory-based hyperspectral imaging methods (400–1000 nm) for predicting proportions of six fatty acids, ratios of saturated and unsaturated fatty acids, and the concentrations of 14 mineral nutrients in Hass avocado fruit from 219 flesh and 194 skin images. Partial least squares regression (PLSR) models predicted the ratio of unsaturated to saturated fatty acids in avocado fruit from both flesh images (R2 = 0.79, ratio of prediction to deviation (RPD) = 2.06) and skin images (R2 = 0.62, RPD = 1.48). The best-fit models predicted parameters that affect postharvest processing such as the ratio of oleic:linoleic acid from flesh images (R2 = 0.67, RPD = 1.63) and the concentrations of boron (B) and calcium (Ca) from flesh images (B: R2 = 0.61, RPD = 1.51; Ca: R2 = 0.53, RPD = 1.71) and skin images (B: R2 = 0.60, RPD = 1.55; Ca: R2 = 0.68, RPD = 1.57). Many quality parameters predicted from flesh images could also be predicted from skin images. Hyperspectral imaging represents a promising tool to reduce postharvest losses of avocado fruit by determining internal fruit quality of individual fruit quickly from flesh or skin images