The global pandemic of COVID-19 that took place in 2020 and 2021 posed different challenges for health systems worldwide, revealing various deficiencies and generating supply problems and a breakdown in medical services. Given this situation, it is crucial to have predictive methodologies that can accurately estimate the behavior of diseases of this type. This would allow countries to be better prepared in the future and respond effectively to future similar situations, avoiding a repetition of large-scale events. In the literature, deep learning techniques, in particular, have shown promise in this field. In this paper, a comparative study is performed between individual Deep Learning models, such as Long Short-Term Memory (LSTM) and Gated Recurrent Units (GRU), along with hybrid models that combine Conv1D with LSTM or GRU. The objective is to predict contagion curves in Latin American countries, specifically in Argentina, Brazil, Chile, Colombia, and Peru. These countries present a dwindling number of studies in the existing literature, which makes this work especially relevant. The results emphasize the competitiveness of the hybrid models, which show MAPE values ranging from 0.1–1%. In contrast, the individual models present slightly higher MAPE, in the range of 0.2–0.8%. These results demonstrate the effectiveness of the proposed Deep Learning models in predicting the spread of COVID-19 in South America.