In this paper, we introduce an optimal quadratic Wiener beamformer for magnitude estimation of a desired signal. For simplicity, we focus on a two-microphone array and develop an iterative algorithm for magnitude estimation based on a quadratic multichannel noise reduction approach. We analyze two test cases, with uncorrelated and correlated noises. In each, we derive the appropriate versions of the Wiener beamformer, as well as their corresponding unbiased magnitude estimators. We compare the root-mean-squared errors (RMSEs) for the linear and quadratic Wiener beamformers and show that for low input signal-to-noise ratios (SNRs), the RMSE obtained with the proposed approach is either lower than or equal to the RMSE obtained with the linear Wiener beamformer, depending on the type of noise and its distribution.