Monkeypox is a double-stranded DNA virus with an envelope and is a member of the Poxviridae family’s Orthopoxvirus genus. This virus can transmit from human to human through direct contact with respiratory secretions, infected animals and humans, or contaminated objects and causing mutations in the human body. In May 2022, several monkeypox affected cases were found in many countries. Because of its transmitting characteristics, on July 23, 2022, a nationwide public health emergency was proclaimed by WHO due to the monkeypox virus. This study analyzed the gene mutation rate that is collected from the most recent NCBI monkeypox dataset. The collected data is prepared to independently identify the nucleotide and codon mutation. Additionally, depending on the size and availability of the gene dataset, the computed mutation rate is split into three categories: Canada, Germany, and the rest of the world. In this study, the genome mutation rate of the monkeypox virus is predicted using a deep learning-based Long Short-Term Memory (LSTM) model and compared with Gated Recurrent Unit (GRU) model. The LSTM model shows “Root Mean Square Error” (RMSE) values of 0.09 and 0.08 for testing and training, respectively. Using this time series analysis method, the prospective mutation rate of the 50^th patient has been predicted. Note that this is a new report on the monkeypox gene mutation. It is found that the nucleotide mutation rates are decreasing, and the balance between bi-directional rates are maintained.