Hand, foot, and mouth disease (HFMD) is a common febrile illness caused by enteroviruses in the Picornaviridae family. The major symptoms of HFMD are fever and a vesicular rash on the hand, foot, or oral mucosa. Acute meningitis and encephalitis are observed in rare cases. HFMD epidemics occur annually in Japan, usually in the summer season. Relatively large-scale outbreaks have occurred every two years since 2011. In this study, the epidemic patterns of HFMD in Japan are predicted four weeks in advance using a deep learning method. The time-series data were analyzed by a long short-term memory (LSTM) approach called a Recurrent Neural Network. The LSTM model was trained on the numbers of weekly HFMD cases in each prefecture. These data are reported in the Infectious Diseases Weekly Report, which compiles the national surveillance data from web sites at the National Institute of Infectious Diseases, Japan, under the Infectious Diseases Control Law. Consequently, our trained LSTM model distinguishes between relatively large-scale and small-scale epidemics. The trained model predicted the HFMD epidemics in 2018 and 2019, indicating that the LSTM approach can estimate the future epidemic patterns of HFMD in Japan.