Superconducting metamaterials formed from arrays of thin-film lumped circuit elements provide a route for implementing novel dispersion relations and band structure in a circuit QED environment. We have implemented metamaterial resonators from left-handed transmission lines and characterized their dense spectrum of modes through a combination of microwave transmission measurements and laser scanning microscopy imaging of the standing-wave structure on the various resonances. By appending a segment of a conventional transmission line on one end of our metamaterial, we have coupled a flux-tunable transmon qubit to the structure and observed the interaction of the qubit with the metamaterial by tuning its transition frequency through resonance with each of the modes. Through time-domain qubit measurements at different flux bias points, we are able to explore the variation in the qubit relaxation time as a function of frequency, with significant dips in lifetime as the qubit transition approaches each mode and a recovery of the lifetime in between resonances. In addition, we have measured the Stark shift of the qubit transition as we drive the metamaterial with different powers on each of its resonances that are coupled to the qubit.