Hyperspectral imaging in optical microscopy is of importance in the study of various submicron physical and chemical phenomena. However, its practical application is still challenging because the additional spectral dimension increases the number of sampling points to be independently measured compared to two-dimensional (2D) imaging. Here, we present a hyperspectral microscopy system through passive illumination approach based on compressive sensing (CS) using a spectrometer with a one-dimensional (1D) detector array and a digital micromirror device (DMD). The illumination is patterned after the sample rather than on it, making this technique compatible with both dark-field and bright-field imaging. The DMD diffraction issue resulting from this approach has been overcome by a novel striped DMD pattern modulation method. In addition, a split pattern method is developed for increasing the spatial resolution when employing the DMD pattern modulation. The efficacy of the system is demonstrated on nanoparticles using two model systems: extended plasmonic metal nanostructures and fluorescent microspheres. The compressive hyperspectral microscopic system provides a fast, high dynamic range, and enhanced signal-to-noise ratio (SNR) platform that yields a powerful and low-cost spectral analytical system to probe the optical properties of a myriad of nanomaterial systems. The system can also be extended to wavelengths beyond the visible spectrum with greatly reduced expense compared to other approaches that use 2D array detectors.