Medical image segmentation is a vital healthcare endeavor requiring precise and efficient models for appropriate diagnosis and treatment. Vision transformer-based segmentation models have shown great performance in accomplishing this task. However, to build a powerful backbone, the self-attention block of ViT requires large-scale pre-training data. The present method of modifying pre-trained models entails updating all or some of the backbone parameters. This paper proposes a novel fine-tuning strategy for adapting a pretrained transformer-based segmentation model on data from a new medical center. This method introduces a small number of learnable parameters, termed prompts, into the input space (less than 1\% of model parameters) while keeping the rest of the model parameters frozen. Extensive studies employing data from new unseen medical centers show that prompts-based fine-tuning of medical segmentation models provides excellent performance on the new center data with a negligible drop on the old centers. Additionally, our strategy delivers great accuracy with minimum re-training on new center data, significantly decreasing the computational and time costs of fine-tuning pre-trained models.