Accurate and automatic segmentation of fibroglandular tissue in breast MRI screening is essential for the quantification of breast density and background parenchymal enhancement. In this retrospective study, we developed and evaluated a transformer-based neural network for breast segmentation (TraBS) in multi-institutional MRI data, and compared its performance to the well established convolutional neural network nnUNet. TraBS and nnUNet were trained and tested on 200 internal and 40 external breast MRI examinations using manual segmentations generated by experienced human readers. Segmentation performance was assessed in terms of the Dice score and the average symmetric surface distance. The Dice score for nnUNet was lower than for TraBS on the internal testset (0.909 ± 0.069 versus 0.916 ± 0.067, P < 0.001) and on the external testset (0.824 ± 0.144 versus 0.864 ± 0.081, P = 0.004). Moreover, the average symmetric surface distance was higher (= worse) for nnUNet than for TraBS on the internal (0.657 ± 2.856 versus 0.548 ± 2.195, P = 0.001) and on the external testset (0.727 ± 0.620 versus 0.584 ± 0.413, P = 0.03). Our study demonstrates that transformer-based networks improve the quality of fibroglandular tissue segmentation in breast MRI compared to convolutional-based models like nnUNet. These findings might help to enhance the accuracy of breast density and parenchymal enhancement quantification in breast MRI screening.