Using the example of Zn-doped La2CuO4, we demonstrate that a spinless impurity doped into a nonfrustrated antiferromagnet can induce substantial frustrating interactions among the spins surrounding it. This result is the key to resolving discrepancies between experimental data and earlier theories. Analytic and quantum Monte Carlo studies of the impurity-induced frustration are in a close accord with each other and experiments. The proposed mechanism should be common to other correlated oxides.