We study the dynamics of quantum discord of a two-qubit system coupled to a common structured reservoir at zero temperature. The conditions to maximize reservoir-induced quantum discord for the two-qubit system wiht an initially factorized state are derived. In particular, when the two qubits are placed in a lossy cavity, high values of quantum discord can be obtained in the dispersive regime, even in the bad-cavity limit. Finally, we show that under certain conditions, the quantum discord dynamics exhibits quantum beats.