This article proposes and evaluates a technique to predict the level of interference in wireless networks. We design a recursive predictor that computes future interference values at a given location by filtering measured interference at this location. The parametrization of the predictor 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 good performance in terms of accuracy between predicted and true values for relevant time horizons. Although the predictor is parametrized for the case of Poisson networks, Rayleigh fading, and fixed message lengths, a sensitivity analysis shows that it also works well in more general network scenarios. Numerical examples for underlay device-to-device communications and a common wireless sensor technology illustrate its broad applicability. The predictor can be applied as part of interference management to improve medium access, scheduling, and resource allocation.