Healthcare federated learning requires strong privacy guarantees while maintaining computational efficiency across resource-constrained medical institutions. This paper presents MedHE, a novel framework combining adaptive gradient sparsification with CKKS homomorphic encryption to enable privacy-preserving collaborative learning on sensitive medical data. Our approach introduces a dynamic threshold mechanism with error compensation for top-k gradient selection, achieving 97.5 percent communication reduction while preserving model utility. We provide formal security analysis under Ring Learning with Errors assumptions and demonstrate differential privacy guarantees with epsilon less than or equal to 1.0. Statistical testing across 5 independent trials shows MedHE achieves 89.5 percent plus or minus 0.8 percent accuracy, maintaining comparable performance to standard federated learning (p=0.32) while reducing communication from 1277 MB to 32 MB per training round. Comprehensive evaluation demonstrates practical feasibility for real-world medical deployments with HIPAA compliance and scalability to 100 plus institutions.