We numerically show that laser-wakefield accelerated electron beams obtained using a PetaWatt-scale laser system can produce high-flux sources of relativistic muons that are suitable for radiographic applications. Scalings of muon energy and flux with the properties of the wakefield electron beams are presented. Applying these results to the expected performance of the 10-PW class laser at the Extreme Light Infrastructure Nuclear Physics (ELI-NP) demonstrates that ultra-high power laser facilities currently in the commissioning phase can generate ultra-relativistic muon beams with more than 104 muons per shot reaching the detector plane. Simple magnetic beamlines are shown to be effective in separating the muons from noise, allowing for their detection using, for example, silicon-based detectors. It is shown that a laser facility like the one at ELI-NP can produce high-fidelity and spatially resolved muon radiographs of enclosed strategically sensitive materials in a matter of minutes.