Menisci are cartilaginous tissue found within the knee that contribute to joint lubrication and weight dispersal. Damage to menisci can lead to onset and progression of knee osteoarthritis (OA), a condition that is a leading cause of disability, and for which there are few effective therapies. Accurate automated segmentation of menisci would allow for earlier detection and treatment of meniscal abnormalities, as well as shedding more light on the role the menisci play in OA pathogenesis. Focus in this area has mainly used variants of convolutional networks, but there has been no attempt to utilise recent large vision transformer segmentation models. The Segment Anything Model (SAM) is a so-called foundation segmentation model, which has been found useful across a range of different tasks due to the large volume of data used for training the model. In this study, SAM was adapted to perform fully-automated segmentation of menisci from 3D knee magnetic resonance images. A 3D U-Net was also trained as a baseline. It was found that, when fine-tuning only the decoder, SAM was unable to compete with 3D U-Net, achieving a Dice score of $0.81\pm0.03$, compared to $0.87\pm0.03$, on a held-out test set. When fine-tuning SAM end-to-end, a Dice score of $0.87\pm0.03$ was achieved. The performance of both the end-to-end trained SAM configuration and the 3D U-Net were comparable to the winning Dice score ($0.88\pm0.03$) in the IWOAI Knee MRI Segmentation Challenge 2019. Performance in terms of the Hausdorff Distance showed that both configurations of SAM were inferior to 3D U-Net in matching the meniscus morphology. Results demonstrated that, despite its generalisability, SAM was unable to outperform a basic 3D U-Net in meniscus segmentation, and may not be suitable for similar 3D medical image segmentation tasks also involving fine anatomical structures with low contrast and poorly-defined boundaries.