Retinal images acquired using fundus cameras are often visually blurred due to imperfect imaging conditions, refractive medium turbidity, and motion blur. In addition, ocular diseases such as the presence of cataract also result in blurred retinal images. The presence of blur in retinal fundus images reduces the effectiveness of the diagnosis process of an expert ophthalmologist or a computer-aided detection/diagnosis system. In this paper, we put forward a single-shot deep image prior (DIP)-based approach for retinal image enhancement. Unlike typical deep learning-based approaches, our method does not require any training data. Instead, our DIP-based method can learn the underlying image prior while using a single degraded image. To perform retinal image enhancement, we frame it as a layer decomposition problem and investigate the use of two well-known analytical priors, i.e., dark channel prior (DCP) and bright channel prior (BCP) for atmospheric light estimation. We show that both the untrained neural networks and the pretrained neural networks can be used to generate an enhanced image while using only a single degraded image. We evaluate our proposed framework quantitatively on five datasets using three widely used metrics and complement that with a subjective qualitative assessment of the enhancement by two expert ophthalmologists. We have compared our method with a recent state-of-the-art method cofe-Net using synthetically degraded retinal fundus images and show that our method outperforms the state-of-the-art method and provides a gain of 1.23 and 1.4 in average PSNR and SSIM respectively. Our method also outperforms other works proposed in the literature, which have evaluated their performance on non-public proprietary datasets, on the basis of the reported results.