In this study, spectral data within the wavelength range of 400–780 nm were used to evaluate the ripeness stages of achacha fruits. The ripeness status of achacha fruits was divided into seven stages. Both average and pixel-based approaches were used to assess the ripeness. The accuracy and n-level-error accuracy of each ripeness stage was predicted by using classification models (Support Vector Machine (SVM), Partial Least Square Discriminant Analysis (PLS-DA), Artificial Neural Network (ANN) and K-Nearest Neighbor (KNN)) and regression models (Partial Least Square Regression (PLSR) and Support Vector Regression (SVR)). Furthermore, how the curvature of the fruit surface affected the prediction of the ripeness stage was investigated. With the use of an averaged spectrum of fruit samples, the accuracy of the model used in this study ranged from 52.25% to 79.75%, and the one-level error accuracy (94.75–100%) was much higher. The SVM model had the highest accuracy (79.75%), and the PLSR model had the highest one-level error accuracy (100%). With the use of pixel-based ripeness prediction results and majority rule, the accuracy (58.25–79.50%) and one-level-error accuracy (95.25–99.75%) of all models was comparable with the accuracy predicted by using averaged spectrum. The pixel-based prediction results showed that the curvature of the fruit could have a noticeable effect on the ripeness evaluation values of achacha fruits with a low or high ripeness stage. Thus, using the spectral data in the central region of achacha fruits would be a relatively reliable choice for ripeness evaluation. For an achacha fruit, the ripeness value of the fruit face exposed to sunlight could be one level higher than that of the face in shadow. Furthermore, when the ripeness value of achacha fruit was close to the mid-value of two adjacent ripeness stage values, all models had a high chance of having one-level ripeness errors. Thus, using a model with high one-level error accuracy for sorting would be a practical choice for the postharvest processing of achacha fruits.