The detection of moons around extrasolar planets is one of the main focuses of current and future observatories. These silent companions contribute to the planets' observed signals but are barely detectable with current methods. Numerous gaseous exoplanets are known to orbit in the habitable zones of stars, and the expected abundance of natural satellites and their diversity in composition make them ideal targets when looking for habitable celestial bodies. Moreover, moons are suspected to play key roles in stabilizing a planet's rotational axis and hence its climate. We show that an exomoon orbiting an Earth-like exoplanet could be identified by measuring the flux and polarization of starlight reflected by the planet-moon system, allowing the characterization of their orbital motions and physical properties.