Although deep learning (DL) has achieved notable progress in speech enhancement (SE), further research is still required for a DL-based SE system to adapt effectively and efficiently to particular speakers. In this study, we propose a novel meta-learning-based speaker-adaptive SE approach (called OSSEM) that aims to achieve SE model adaptation in a one-shot manner. OSSEM consists of a modified transformer SE network and a speaker-specific masking (SSM) network. In practice, the SSM network takes an enrolled speaker embedding extracted using ECAPA-TDNN to adjust the input noisy feature through masking. To evaluate OSSEM, we designed a modified Voice Bank-DEMAND dataset, in which one utterance from the testing set was used for model adaptation, and the remaining utterances were used for testing the performance. Moreover, we set restrictions allowing the enhancement process to be conducted in real time, and thus designed OSSEM to be a causal SE system. Experimental results first show that OSSEM can effectively adapt a pretrained SE model to a particular speaker with only one utterance, thus yielding improved SE results. Meanwhile, OSSEM exhibits a competitive performance compared to state-of-the-art causal SE systems.