Light sheet fluorescence microscopy (LSFM) is a widely used technique for imaging cleared tissues and living samples. However, like most filter-based fluorescence techniques, LSFM cannot quantitatively image samples with autofluorescence or multiple fluorophores with overlapping spectra. In this study, we introduce hyperspectral structured LSFM that combines structured illumination in one spatial dimension with a data-driven algorithm based on a neural network and a physical model of the acquisition process. Our hyperspectral structured LSFM approach enables the robust reconstruction of hyperspectral data in samples with multiple fluorophores, in addition to the quantitative estimation of the abundance of each fluorophore present. We demonstrate the efficiency of our hyperspectral structured LSFM approach by imaging zebrafish embryos in 3D, illustrating autofluorescence removal and the separation of two spectrally overlapping red fluorophores. Hyperspectral structured LSFM paves the way for versatile high-resolution, quantitative hyperspectral imaging in biomedical research.