The COVID-19 death rate in Northeast Brazil is much higher when compared to the national average, demanding a study into the prognosis of the region for planning control measures and preventing the collapse of the health care system. We estimated the potential total cumulative cases of COVID-19 in the region for the next three months. Our study included all confirmed cases, from March 8 until April 28, 2020, collected from the official website that reports the situation of COVID-19 infections in Brazil. The Boltzmann function was applied to a data simulation for each set of data regarding different states. The model data were well fitted, with R2 values close to 0.999. Up to April 28, 20,665 cases were confirmed in the region. The state of Ceará has the highest rate of accumulated cases per 100,000 inhabitants (75.75), followed by Pernambuco. We estimated that the states of Ceará, Sergipe and Paraíba will experience a dramatic increase in the rate of cumulative cases until July 31. Maranhão, Pernambuco, Rio Grande do Norte and Piauí showed a more discreet increase in the model. For Bahia and Alagoas, a 4.7 and 6.6-fold increase in the rate was estimated, respectively. We estimate a substantial increase in the rate of cumulative cases per 100,000 inhabitants in the region within three months, especially for Ceará, Sergipe and Paraíba. The Boltzmann function proved to be a simple tool for epidemiological forecasting that can help planning the measures to contain COVID-19.