Japan has observed a surge in the number of confirmed cases of the coronavirus disease (COVID-19) that has caused a serious impact on the society especially after the declaration of the state of emergency on April 7, 2020. This study analyzes the real time data from March 1 to April 22, 2020 by adopting a sophisticated statistical modeling based on the state space model combined with the well-known susceptible-infected-recovered (SIR) model. The model estimation and forecasting are conducted using the Bayesian methodology. The present study provides the parameter estimates of the unknown parameters that critically determine the epidemic process derived from the SIR model and prediction of the future transition of the infectious proportion including the size and timing of the epidemic peak with the prediction intervals that naturally accounts for the uncertainty. Even though the epidemic appears to be settling down during this intervention period, the prediction results under various scenarios using the data up to May 18 reveal that the temporary reduction in the infection rate would still result in a delayed the epidemic peak unless the long-term reproduction number is controlled.