The recent development of Deep Neural Networks (DNN) has significantly increased the realism of AI-synthesized faces, with the most notable examples being the DeepFakes. The DeepFake technology can synthesize a face of target subject from a face of another subject, while retains the same face attributes. With the rapidly increased social media portals (Facebook, Instagram, etc), these realistic fake faces rapidly spread though the Internet, causing a broad negative impact to the society. In this paper, we describe Landmark Breaker, the first dedicated method to disrupt facial landmark extraction, and apply it to the obstruction of the generation of DeepFake videos.Our motivation is that disrupting the facial landmark extraction can affect the alignment of input face so as to degrade the DeepFake quality. Our method is achieved using adversarial perturbations. Compared to the detection methods that only work after DeepFake generation, Landmark Breaker goes one step ahead to prevent DeepFake generation. The experiments are conducted on three state-of-the-art facial landmark extractors using the recent Celeb-DF dataset.