The ridge inverse covariance estimator is generalized to allow for entry-wise penalization. An efficient algorithm for its evaluation is proposed. Its computational accuracy is benchmarked against implementations of specific cases the generalized ridge inverse covariance estimator encompasses. The proposed estimator shrinks toward a user-specified, nonrandom target matrix and is shown to be positive definite and consistent. It is pointed out how the generalized ridge inverse covariance estimator can be used to obtain a generalization of the graphical lasso estimator as well as of its elastic net counterpart. The usage of the presented estimator is illustrated in graphical modeling of omics data. Supplementary materials for this article are available online.