This paper presents FreD, a novel parameterization method for dataset distillation, which utilizes the frequency domain to distill a small-sized synthetic dataset from a large-sized original dataset. Unlike conventional approaches that focus on the spatial domain, FreD employs frequency-based transforms to optimize the frequency representations of each data instance. By leveraging the concentration of spatial domain information on specific frequency components, FreD intelligently selects a subset of frequency dimensions for optimization, leading to a significant reduction in the required budget for synthesizing an instance. Through the selection of frequency dimensions based on the explained variance, FreD demonstrates both theoretical and empirical evidence of its ability to operate efficiently within a limited budget, while better preserving the information of the original dataset compared to conventional parameterization methods. Furthermore, based on the orthogonal compatibility of FreD with existing methods, we confirm that FreD consistently improves the performances of existing distillation methods over the evaluation scenarios with different benchmark datasets. We release the code at https://github.com/sdh0818/FreD.