Enhancing speech captured by distant microphones is a challenging task. In this study, we investigate the multichannel signal properties of the single acoustic vector sensor (AVS) to obtain the inter-sensor data ratio (ISDR) model in the time-frequency (TF) domain. Then, the monotone functions describing the relationship between the ISDRs and the direction of arrival (DOA) of the target speaker are derived. For the target speech enhancement (SE) task, the DOA of the target speaker is given, and the ISDRs are calculated. Hence, the TF components dominated by the target speech are extracted with high probability using the established monotone functions, and then, a nonlinear soft mask of the target speech is generated. As a result, a masking-based speech enhancement method is developed, which is termed the AVS-SMASK method. Extensive experiments with simulated data and recorded data have been carried out to validate the effectiveness of our proposed AVS-SMASK method in terms of suppressing spatial speech interferences and reducing the adverse impact of the additive background noise while maintaining less speech distortion. Moreover, our AVS-SMASK method is computationally inexpensive, and the AVS is of a small physical size. These merits are favorable to many applications, such as robot auditory systems.