This article proposes and evaluates a technique to predict the level of interference in wireless networks. We design a recursive predictor that estimates future interference values by filtering measured interference at a given location. The predictor's parameterization is done offline by translating the autocorrelation of interference into an autoregressive moving average (ARMA) representation. This ARMA model is inserted into a steady-state Kalman filter enabling nodes to predict with low computational effort. Results show a good accuracy of predicted values versus true values for relevant time horizons. Although the predictor is parameterized for Poisson-distributed nodes, Rayleigh fading, and fixed message lengths, a sensitivity analysis shows that it also tends to work well in more general network scenarios. Numerical examples for underlay device-to-device communications, a common wireless sensor technology, and coexistence scenarios of Wi-Fi and LTE illustrate its broad applicability. The predictor can be applied as part of interference management to improve medium access, scheduling, and radio resource allocation.