Billions of people share images from their daily lives on social media every day. However, their biometric information (e.g., fingerprints) could be easily stolen from these images. The threat of fingerprint leakage from social media has created a strong desire to anonymize shared images while maintaining image quality, since fingerprints act as a lifelong individual biometric password. To guard the fingerprint leakage, adversarial attack that involves adding imperceptible perturbations to fingerprint images have emerged as a feasible solution. However, existing works of this kind are either weak in black-box transferability or cause the images to have an unnatural appearance. Motivated by the visual perception hierarchy (i.e., high-level perception exploits model-shared semantics that transfer well across models while low-level perception extracts primitive stimuli that result in high visual sensitivity when a suspicious stimulus is provided), we propose FingerSafe, a hierarchical perceptual protective noise injection framework to address the above mentioned problems. For black-box transferability, we inject protective noises into the fingerprint orientation field to perturb the model-shared high-level semantics (i.e., fingerprint ridges). Considering visual naturalness, we suppress the low-level local contrast stimulus by regularizing the response of the Lateral Geniculate Nucleus. Our proposed FingerSafe is the first to provide feasible fingerprint protection in both digital (up to 94.12%) and realistic scenarios (Twitter and Facebook, up to 68.75%). Our code can be found at https://github.com/nlsde-safety-team/FingerSafe.