In the digital holographic measurement system, the speckle noise introduced during recording severely affects the hologram quality, leading to errors in the three-dimensional (3D) reconstruction results. Phase extraction is instrumental in affecting accuracy in a digital holographic 3D measurement system, and the result of phase unwrapping is crucial in obtaining the correct continuous phase. To suppress the speckle noise in the digital holographic measurement system, this study proposes a suppression method dealing with the wrapped phase. A two-dimensional Gaussian window was used to locally analyze the wrapped phase in the frequency domain. The threshold was selected based on the high correlation between the window Fourier basis function and wrapped phase. According to the threshold, the noise spectrum was discarded to obtain the wrapped phase with low speckle noise. The digital holographic measurement system with effective speckle noise suppression was realized using the microlens array as the test object. Results show that the proposed method protects the 2π jump boundary of the wrapped phase and can effectively improve the 3D reconstruction accuracy of the digital holographic measurement system. Compared with the unfiltered result, the residual error of the proposed method is reduced by 28.35% (peak valley) and 20.23% (root mean square).