Contrast-enhanced digital mammography (CEDM) is an alternative to conventional X-ray mammography for imaging dense breasts. However, conventional approaches to CEDM require a double exposure of the patient, implying higher dose, and risk of incorrect image registration due to motion artifacts. A novel approach is presented, based on hyperspectral imaging, where a detector combining positional and high-resolution spectral information (in this case based on Cadmium Telluride) is used. This allows simultaneous acquisition of the two images required for CEDM. The approach was tested on a custom breast-equivalent phantom containing iodinated contrast agent (Niopam 150®). Two algorithms were used to obtain images of the contrast agent distribution: K-edge subtraction (KES), providing images of the distribution of the contrast agent with the background structures removed, and a dual-energy (DE) algorithm, providing an iodine-equivalent image and a water-equivalent image. The high energy resolution of the detector allowed the selection of two close-by energies, maximising the signal in KES images, and enhancing the visibility of details with the low surface concentration of contrast agent. DE performed consistently better than KES in terms of contrast-to-noise ratio of the details; moreover, it allowed a correct reconstruction of the surface concentration of the contrast agent in the iodine image. Comparison with CEDM with a conventional detector proved the superior performance of hyperspectral CEDM in terms of the image quality/dose tradeoff.