We report the design and application of a prism-based detection system for fluorescence (cross) correlation spectroscopy. The system utilizes a single laser wavelength for the simultaneous excitation of several dyes of different emission spectra. Fluorescence light is spectrally separated with a prismatic setup, and wavelengths are selected by scanning a fiber-coupled avalanche photodiode across the image spots. Multicolor autocorrelations are demonstrated with standard and tandem dyes, and fluorescence cross-correlation measurements of biotinylated nanocontainers and streptavidin are presented. This spectrometer offers high optical stability and no focal volume mismatch for the multicolor detection of molecular dynamics and interactions, with single-molecule sensitivity.