Poor-quality retinal images do not allow an accurate medical diagnosis, and it is inconvenient for a patient to return to a medical center to repeat the fundus photography exam. In this paper, a robust automatic system is proposed to assess the quality of retinal images at the moment of the acquisition, aiming at assisting health care professionals during a fundus photography exam. We propose a convolutional neural network (CNN) pretrained on non-medical images for extracting general image features. The weights of the CNN are further adjusted via a fine-tuning procedure, resulting in a performant classifier obtained only with a small quantity of labeled images. The CNN performance was evaluated on two publicly available databases (i.e., DRIMDB and ELSA-Brasil) using two different procedures: intra-database and inter-database cross-validation. The CNN achieved an area under the curve (AUC) of 99.98% on DRIMDB and an AUC of 98.56% on ELSA-Brasil in the inter-database experiment, where training and testing were not performed on the same database. These results show the robustness of the proposed model to various image acquisitions without requiring special adaptation, thus making it a good candidate for use in operational clinical scenarios.