To monitor the micro-nano-scale deformation of optical fiber material during industrial production, this paper proposes a novel method based on the digital speckle correlation method (DSCM) to measure the out-of-plane displacement. The in-plane displacements between two consecutive images before and after material deformation are estimated by the DSCM. Then, the out-of-plane displacement field of optical fiber material under a microscope can be obtained by the wedge model. The principle of the DSCM is introduced and the measurement of out-of-plane displacement for the optical fiber material is simulated and tested based on the image spherizing algorithm. Simulation and experimental results show that the proposed method can directly extract the out-of-plane displacement from the in-plane displacement of two-dimensional images and measure the real-time deformation of optical fiber material. The experimental device used by the method is quite simple, and only an industrial camera is needed to capture two images under a microscope and thus complete the measurement. Furthermore, the out-of-plane displacement extraction process needs neither conversion of the images to the frequency domain nor phase envelope operation. The proposed method is appropriate for dynamic measurement.