Non-invasive optical imaging techniques, such as optical coherence tomography, are essential diagnostic tools in many disciplines, from the life sciences to nanotechnology. However, present methods are not able to image through opaque layers that scatter all the incident light. Even a very thin layer of a scattering material can appear opaque and hide any objects behind it. Although great progress has been made recently with methods such as ghost imaging and wavefront shaping, present procedures are still invasive because they require either a detector or a nonlinear material to be placed behind the scattering layer. Here we report an optical method that allows non-invasive imaging of a fluorescent object that is completely hidden behind an opaque scattering layer. We illuminate the object with laser light that has passed through the scattering layer. We scan the angle of incidence of the laser beam and detect the total fluorescence of the object from the front. From the detected signal, we obtain the image of the hidden object using an iterative algorithm. As a proof of concept, we retrieve a detailed image of a fluorescent object, comparable in size (50 micrometres) to a typical human cell, hidden 6 millimetres behind an opaque optical diffuser, and an image of a complex biological sample enclosed between two opaque screens. This approach to non-invasive imaging through strongly scattering media can be generalized to other contrast mechanisms and geometries.