The Memetic Differential Evolution Clustering (MDEClust) algorithm represents a state-of-the-art approach for solving the Minimum Sum-of-Squares Clustering (MSSC) problem for small to medium-scale datasets, delivering superior clustering quality. However, its sequential nature limits scalability and computational efficiency. We propose Parallel Memetic Differential Evolution Clustering (Parallel MDEClust) to efficiently solve the MSSC problem, combining global and local search via Differential Evolution and K-means. To our knowledge, this is the first parallel adaptation of a memetic Differential Evolution approach for MSSC, combining population-level recombination and K-means local search under a unified parallel framework. Parallel MDEClust significantly reduces runtime, achieving an average reduction of 52.05% across 18 benchmark datasets and up to 95% reduction in large-scale cases, while preserving or improving clustering quality in 79% of test cases. By exploiting population-level parallelism, it enhances both scalability and accuracy, demonstrating practical value for machine learning, data mining, and pattern recognition.