<p>In small-scale superconducting quantum processors based on the circuit quantum electrodynamics (cQED) architecture, the qubit is typically modeled as coupled to a broad-band, nearly structure-less environment (frequency-independent or slowly varying in frequency), leading to dynamics that is well-approximated by the Markovian approximation. This approximation is usually facilitated by the large detuning between the qubit and the read-out resonator. However, when these systems are scaled up, parasitic couplings between a given qubit and the read-out resonators of the other qubits become unavoidable. In such a case, a qubit experiences a structured (frequency-dependent) environment of the parasitic resonators, some of which may have small detunings, thereby leading to the break-down of the Markovian approximation. In this article, we numerically investigate the effect of such parasitic modes coupled to a qubit for parameters typical of cQED systems. We observe that non-Markovian effects become more pronounced as the resonators are populated with more photons, suggesting that readout of one qubit can parasitically induce non-Markovian behavior in neighboring qubits. We qualitatively analyze the dependence of non-Markovianity on system parameters such as photon number, coupling strength, and detuning, and identify distinct regimes, hence characterizing the non-Markovian behavior which is quantified using simulations computing the trace-distance metric.</p>