The first case of the novel coronavirus in Brazil was notified on February 26, 2020. After 21 days, the first case was reported in the second largest State of the Brazilian Amazon. The State of Pará presented difficulties in combating the pandemic, ranging from underreporting and a low number of tests to a large territorial distance between cities with installed hospital capacity. Due to these factors, mathematical data-driven short-term forecasting models can be a promising initiative to assist government officials in more agile and reliable actions. This study presents an approach based on artificial neural networks for the daily and cumulative forecasts of cases and deaths caused by COVID-19, and the forecast of demand for hospital beds. Six scenarios with different periods were used to identify the quality of the generated forecasting and the period in which they start to deteriorate. Results indicated that the computational model adapted capably to the training period and was able to make consistent short-term forecasts, especially for the cumulative variables and for demand hospital beds.