Head avatar generation is facilitated to construct high-fidelity 3D virtual personas from a single portrait, but it also raises the risk of unauthorized personal avatars generation. Recent 2D portrait protection methods actively prevent malicious image generation by perturbing the identity features. However, there are two key limitations when directly applied to prevent 3D head avatar generation: 1) These methods neglect the inherent 3D geometric structure of portrait, thus failing to disrupt the modeling of 3D shapes or poses. 2) They focus only on identity offset and are unable to interfere with the overall appearance, resulting in excessive preservation of facial characteristics. To overcomes these limitations, we propose a 3D defense framework termed Anti-Avatar, tailored to protect against unauthorized 3D head avatar generation from a single portrait. Specifically, Anti-Avatar consists of two key designs: Geometric Disruption and Perceptual Confusion. The former disrupts the precise reconstruction of 3D structure by interfering with the estimation of geometric parameters, thus affecting the structural accuracy of the 3D avatar. Collaboratively, the latter confuses image features by dispersing attention distribution, thereby hindering the effective perception of portrait appearance. Benefiting from the above dual-space divergence in geometry and perception, the avatars generated by our protected portraits exhibit substantial discrepancies from the originals. Extensive experiments show that our Anti-Avatar outperforms 2D methods in protection performance and effectively resists reconstruction and manipulation by state-of-the-art 3D head avatar generation methods.