We propose and demonstrate two mitigation methods to attenuate the cosmic muon flux compatible with experiments involving superconducting qubits. Using a specifically-built cosmic muon detector, we find that chips oriented towards the horizon compared to chips looking at the sky overhead experience a decrease of a factor 1.6 of muon counts at the surface. Then, we identify shielded shallow underground sites, ubiquitous in urban environments, where significant additional attenuation, up to a factor 35 for 100-meter depths, can be attained. The two methods here described are the first proposed to directly reduce the effects from cosmic rays on qubits by attenuating the noise source, complementing existing on-chip mitigation strategies. We expect that both on-chip and off-chip methods combined will become ubiquitous in quantum technologies based on superconducting qubit circuits.