A modified version of the SEIR model with the effects of vaccination and inter-state movement is proposed to simulate the spread of COVID-19 in Malaysia. A mathematical analysis of the proposed model was performed to derive the basic reproduction number. To enhance the model's forecasting capabilities, the model parameters were estimated using the Nelder-Mead simplex method by fitting the model outputs to the observed data. Our results showed a good fit between the model outputs and available data, where the model was then able to perform short-term predictions. In line with the rapid vaccination program, our model predicted that the COVID-19 cases in the country would decrease by the end of August. Furthermore, our findings indicated that relaxing travel restrictions from a highly vaccinated region to a low vaccinated region would result in an epidemic outbreak.