We present a subword regularization method for WordPiece, which uses a maximum matching algorithm for tokenization. The proposed method, MaxMatch-Dropout, randomly drops words in a search using the maximum matching algorithm. It realizes finetuning with subword regularization for popular pretrained language models such as BERT-base. The experimental results demonstrate that MaxMatch-Dropout improves the performance of text classification and machine translation tasks as well as other subword regularization methods. Moreover, we provide a comparative analysis of subword regularization methods: subword regularization with SentencePiece (Unigram), BPE-Dropout, and MaxMatch-Dropout.