In most container terminals, containers are piled up and stored in a yard in order to utilize the space efficiently. Hence, it requires unproductive container-handling operations to retrieve a container that is not placed on the top of a container stack. As a result, to streamline container-loading operations by which containers are transferred from a yard to a vessel, it is necessary to pre-marshal (i.e., shuffle in advance) containers in accordance with container-loading plan. We propose $A^*$ algorithm to find the optimal container-relocation sequence for the intra-bay container pre-marshalling problem. To work out the heuristic estimate for the proposed $A^*$ algorithm, we introduce the container rearrangement problem and obtain the lower bound of the length of the optimal relocation sequence. The performance of the algorithm is validated extensively by the numerical experiments on the problem instances that are given in the previous studies and generated randomly with various parameters.