This LNCS conference set constitutes the proceedings of the First Medical Image Segmentation Challenge, MedSAM on Laptop 2024, Held in Conjunction with CVPR 2024, in Seattle, WA, USA, held in June 2024. The 16 full papers presented were thoroughly reviewed and selected from the 200 submissions. This challenge aims to prompt the development of universal promotable medical image segmentation foundation models that are deployable on laptops or other edge devices without reliance on GPUs.