The substantial increase in the number of daily new cases infected with coronavirus around the world is alarming, and several researchers are currently using various mathematical and machine learning-based prediction models to estimate the future trend of this pandemic. In this work, we employed the Autoregressive Integrated Moving Average (ARIMA) model to forecast the expected daily number of COVID-19 cases in Saudi Arabia in the next four weeks. We first performed four different prediction models; Autoregressive Model, Moving Average, a combination of both (ARMA), and integrated ARMA (ARIMA), to determine the best model fit, and we found out that the ARIMA model outperformed the other models. The forecasting results showed that the trend in Saudi Arabia will continue growing and may reach up to 7668 new cases per day and over 127,129 cumulative daily cases in a matter of four weeks if stringent precautionary and control measures are not implemented to limit the spread of COVID-19. This indicates that the Umrah and Hajj Pilgrimages to the two holy cities of Mecca and Medina in Saudi Arabia that are supposedly scheduled to be performed by nearly 2 million Muslims in mid-July may be suspended. A set of extreme preventive and control measures are proposed in an effort to avoid such a situation.