Drug discovery (DD) is a time-consuming and expensive process. Thus, the industry employs strategies such as drug repositioning and drug repurposing, which allows the application of already approved drugs to treat a different disease, as occurred in the first months of 2020, during the COVID-19 pandemic. The prediction of drug–target interactions is an essential part of the DD process because it can accelerate it and reduce the required costs. DTI prediction performed in silico have used approaches based on molecular docking simulations, including similarity-based and network- and graph-based ones. This paper presents MPS2IT-DTI, a DTI prediction model obtained from research conducted in the following steps: the definition of a new method for encoding molecule and protein sequences onto images; the definition of a deep-learning approach based on a convolutional neural network in order to create a new method for DTI prediction. Training results conducted with the Davis and KIBA datasets show that MPS2IT-DTI is viable compared to other state-of-the-art (SOTA) approaches in terms of performance and complexity of the neural network model. With the Davis dataset, we obtained 0.876 for the concordance index and 0.276 for the MSE; with the KIBA dataset, we obtained 0.836 and 0.226 for the concordance index and the MSE, respectively. Moreover, the MPS2IT-DTI model represents molecule and protein sequences as images, instead of treating them as an NLP task, and as such, does not employ an embedding layer, which is present in other models.