Brain metastases are a serious form of brain cancer that can significantly shorten a patient's life expectancy. Accurately detecting and tracking the volume of metastatic lesions is critical for patient prognosis. While transformer methods have been shown to be effective in natural images, they require large and annotated datasets to achieve state-of-the-art performance. Convolutional neural networks (CNNs), on the other hand, are easier to train and can achieve high performance even with smaller datasets, making them suitable for medical imaging data. Recently, the ConvNeXt architecture was proposed as a way to modernize the standard CNN by mirroring transformer blocks. In this work, we propose MLP-UNEXT, a hybrid architecture that combines CNNs and multi-layer perceptrons (MLPs) for segmenting brain tumor metastases on MRI scans. We show that MLP-UNEXT achieves state-of-the-art performance on the BRATS METS dataset, outperforming both CNN and transformer methods. MLP-UNEXT also demonstrates faster training and inference speed, lower computational complexity, and higher data-efficiency than other methods. We believe that MLP-UNEXT is a promising new approach for brain metastasis segmentation since it is fast, efficient, and accurate.