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Preoperative determination of implant size for total knee arthroplasty surgery has numerous clinical and logistical benefits. Currently, surgeons use X-ray-based templating to estimate implant size, but this method has low accuracy. Our study aims to improve accuracy by developing a machine learning approach that predicts the required implant size based on a 3D femoral bone mesh, the key factor in determining the correct implant size. A linear regression framework imposing group sparsity on the 3D bone mesh vertex coordinates was proposed based on a dataset of 446 MRI scans. The group sparse regression method was further regularized based on the connectivity of the bone mesh to enforce neighbouring vertices to have similar importance to the model. Our hypergraph regularized group lasso had an accuracy of 70.1% in predicting femoral implant size while the initial implant size prediction provided by the instrumentation manufacturer to the surgeon has an accuracy of 23.1%. Furthermore, our method was capable of predicting the implant size up to one size smaller or larger with an accuracy of 99.1%, thereby surpassing other state-of-the-art methods. The hypergraph regularized group lasso was able to obtain a significantly higher accuracy compared to the implant size prediction provided by the instrumentation manufacturer.