The objective of this work is to perform image quality assessment (IQA) of eye fundus images in the context of digital fundoscopy with topological data analysis (TDA) and machine learning methods. Eye health remains inaccessible for a large amount of the global population. Digital tools that automize the eye exam could be used to address this issue. IQA is a fundamental step in digital fundoscopy for clinical applications; it is one of the first steps in the preprocessing stages of computer-aided diagnosis (CAD) systems using eye fundus images. Images from the EyePACS dataset were used, and quality labels from previous works in the literature were selected. Cubical complexes were used to represent the images; the grayscale version was, then, used to calculate a persistent homology on the simplex and represented with persistence diagrams. Then, 30 vectorized topological descriptors were calculated from each image and used as input to a classification algorithm. Six different algorithms were tested for this study (SVM, decision tree, k-NN, random forest, logistic regression (LoGit), MLP). LoGit was selected and used for the classification of all images, given the low computational cost it carries. Performance results on the validation subset showed a global accuracy of 0.932, precision of 0.912 for label "quality" and 0.952 for label "no quality", recall of 0.932 for label "quality" and 0.912 for label "no quality", AUC of 0.980, F1 score of 0.932, and a Matthews correlation coefficient of 0.864. This work offers evidence for the use of topological methods for the process of quality assessment of eye fundus images, where a relatively small vector of characteristics (30 in this case) can enclose enough information for an algorithm to yield classification results useful in the clinical settings of a digital fundoscopy pipeline for CAD.