One-Shot Federated Learning (OFL) is a promising approach that reduce communication to a single round, minimizing latency and resource consumption. However, existing OFL methods often rely on Knowledge Distillation, which introduce server-side training, increasing latency. While neuron matching and model fusion techniques bypass server-side training, they struggle with alignment when heterogeneous data is present. To address these challenges, we proposed One-Shot Federated Learning with Tsetlin Machine (FedTMOS), a novel data-free OFL framework built upon the low-complexity and class-adaptive properties of the Tsetlin Machine. FedTMOS first clusters then reassigns class-specific weights to form models using an inter-class maximization approach, efficiently generating balanced server models without requiring additional training. Our extensive experiments demonstrate that FedTMOS significantly outperforms its ensemble counterpart by an average of $6.16$%, and the leading state-of-the-art OFL baselines by $7.22$% across various OFL settings. Moreover, FedTMOS achieves at least a $2.3\times$ reduction in upload communication costs and a $75\times$ reduction in server latency compared to methods requiring server-side training. These results establish FedTMOS as a highly efficient and practical solution for OFL scenarios.