Fano resonance is achieved by tuning two coupled oscillators and has exceptional potential for modulating light dispersion. Here, distinct from the classical Fano resonances achieved through photonics methodologies, we introduce the Fano resonance in epsilon-near-zero (ENZ) media with novel electromagnetic properties. By adjusting the background permeability of the ENZ host, the transmission spectrum exhibits various dispersive line shapes and covers the full range of Fano parameter q morphologies, from negative to positive infinity. Furthermore, owing to the stretched electromagnetic waves in the ENZ media, ENZ Fano resonance has geometry-independent characteristics and can even be attained on a subwavelength scale. With the assistance of the Fabry-Perot mode, the background relative permeability of waveguide ENZ media can be engineered, experimentally validating the concept of ENZ Fano resonance. Our Letter has significant implications for electromagnetic metamaterials and photonic devices, with potential applications in exotic dispersion modulation and synthesis of light.