Forecasts can help in the decision-making process. Epidemiological forecasts are no different, they can help to evaluate the scenario and possible direction of disease spread, for guiding possible interventions. In this work, Echo State Networks (ESNs) are evaluated for COVID-19 (Coronavirus Disease 2019) cases and deaths forecasting ten days ahead. The chosen locations for the experiment are five states in Brazil, namely Sao Paulo (SP), Bahia (BA), Minas Gerais (MG), Rio de Janeiro (RJ), and Ceara (CE), the states with the most COVID-19 cases as of December 31, 2020. The results are evaluated using performance indexes RMSE (Root-mean-square error), MAE (Mean absolute error), and MAPE (Mean absolute percentage error). Results are compared with a common forecasting technique called ARIMA (Autoregressive Integrated Moving Average). The error signals are compared using Wilcoxon Signed-Rank Test, to evaluate the difference statistically. ESNs presented overall good results for a ten day horizon forecast regarding used performance metrics, but for the number of cases, ARIMA outperformed ESNs regarding RMSE, MAE, and MAPE in all but one state. For the number of deaths however, ESNs outperformed ARIMA in most states when the MAE is taken into account. ESNs are shown to be a solid forecasting model when compared with ARIMA, presenting comparable results and in some cases outperforming it.