3D deep learning is a growing field of interest due to the vast amount of information stored in 3D formats. Triangular meshes are an efficient representation for irregular, non-uniform 3D objects. However, meshes are often challenging to annotate due to their high geometrical complexity. Specifically, creating segmentation masks for meshes is tedious and time-consuming. Therefore, it is desirable to train segmentation networks with limited-labeled data. Self-supervised learning (SSL), a form of unsupervised representation learning, is a growing alternative to fully-supervised learning which can decrease the burden of supervision for training. We propose SSL-MeshCNN, a self-supervised contrastive learning method for pre-training CNNs for mesh segmentation. We take inspiration from traditional contrastive learning frameworks to design a novel contrastive learning algorithm specifically for meshes. Our preliminary experiments show promising results in reducing the heavy labeled data requirement needed for mesh segmentation by at least 33%.