Hyperspectral Imaging (HSI) is increasingly adopted in medical applications for the usefulness of understanding the spectral signature of specific organic and non-organic elements. The acquisition of such images is a complex task, and the commercial sensors that can measure such images is scarce down to the point that some of them have limited spatial resolution in the bands of interest. This work proposes an approach to enhance the spatial resolution of hyperspectral histology samples using super-resolution. As the data volume associated to HSI has always been an inconvenience for the image processing in practical terms, this work proposes a relatively low computationally intensive algorithm. Using multiple images of the same scene taken in a controlled environment (hyperspectral microscopic system) with sub-pixel shifts between them, the proposed algorithm can effectively enhance the spatial resolution of the sensor while maintaining the spectral signature of the pixels, competing in performance with other state-of-the-art super-resolution techniques, and paving the way towards its use in real-time applications.