Large transformer models, trained on diverse datasets, have demonstrated impressive few-shot performance on previously unseen tasks without requiring parameter updates. This capability has also been explored in Reinforcement Learning (RL), where agents interact with the environment to retrieve context and maximize cumulative rewards, showcasing strong adaptability in complex settings. However, in cooperative Multi-Agent Reinforcement Learning (MARL), where agents must coordinate toward a shared goal, decentralized policy deployment can lead to mismatches in task alignment and reward assignment, limiting the efficiency of policy adaptation. To address this challenge, we introduce Multi-agent In-context Coordination via Decentralized Memory Retrieval (MAICC), a novel approach designed to enhance coordination by fast adaptation. Our method involves training a centralized embedding model to capture fine-grained trajectory representations, followed by decentralized models that approximate the centralized one to obtain team-level task information. Based on the learned embeddings, relevant trajectories are retrieved as context, which, combined with the agents' current sub-trajectories, inform decision-making. During decentralized execution, we introduce a novel memory mechanism that effectively balances test-time online data with offline memory. Based on the constructed memory, we propose a hybrid utility score that incorporates both individual- and team-level returns, ensuring credit assignment across agents. Extensive experiments on cooperative MARL benchmarks, including Level-Based Foraging (LBF) and SMAC (v1/v2), show that MAICC enables faster adaptation to unseen tasks compared to existing methods.