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In this paper, a new denoising method for hyperspectral images is proposed using First Order Roughness Penalty (FORP). FORP is applied in the wavelet domain to exploit the Multi-Resolution Analysis (MRA) property of wavelets. Stein's Unbiased Risk Estimator (SURE) is used to choose the tuning parameters automatically. The simulation results show that the penalized least squares using FORP can improve the Signal to Noise Ratio (SNR) compared to other denoising methods. The proposed method is also applied to a corrupted hyperspectral data set and it is shown that certain classification indices improve significantly.