Quantum - or classically correlated - light can be employed in various ways to improve resolution and measurement sensitivity. In an interaction-free measurement, a single photon can be used to reveal the presence of an object placed within one arm of an interferometer without being absorbed by it. This method has previously been applied to imaging. With a technique known as ghost imaging, entangled photon pairs are used for detecting an opaque object with significantly improved signal-to-noise ratio while preventing over-illumination. Here, we integrate these two methods to obtain a new imaging technique which we term interaction-free ghost-imaging that possesses the benefits of both techniques. While maintaining the image quality of conventional ghost-imaging, this new technique is also sensitive to phase and polarisation changes in the photons introduced by a structured object. Furthermore, thanks to the interaction-free nature of this new technique, it is possible to reduce the number of photons required to produce a clear image of the object (which could be otherwise damaged by the photons) making this technique superior for probing light-sensitive materials and biological tissues.