Multiparametric Magnetic Resonance Imaging (MRI) is the most sensitive imaging modality for breast cancer detection and is increasingly playing a key role in lesion characterization. In this context, accurate and reliable quantification of the shape and extent of breast cancer is crucial in clinical research environments. Since conventional lesion delineation procedures are still mostly manual, automated segmentation approaches can improve this time-consuming and operator-dependent task by annotating the regions of interest in a reproducible manner. In this work, a semi-automated and interactive approach based on the spatial Fuzzy C-Means (sFCM) algorithm is proposed, used to segment masses on dynamic contrast-enhanced (DCE) MRI of the breast. Our method was compared against existing approaches based on classic image processing, namely (i) Otsu's method for thresholding-based segmentation, and (ii) the traditional FCM algorithm. A further comparison was performed against state-of-the-art Convolutional Neural Networks (CNNs) for medical image segmentation, namely SegNet and U-Net, in a 5-fold cross-validation scheme. The results showed the validity of the proposed approach, by significantly outperforming the competing methods in terms of the Dice similarity coefficient (84.47±4.75). Moreover, a Pearson's coefficient of ρ=0.993 showed a high correlation between segmented volume and the gold standard provided by clinicians. Overall, the proposed method was confirmed to outperform the competing literature methods. The proposed computer-assisted approach could be deployed into clinical research environments by providing a reliable tool for volumetric and radiomics analyses.