Cardiovascular disease (CVD) is a leading cause of morbidity and mortality worldwide, necessitating early detection and accurate risk assessment. Low-dose computed tomography (LDCT) chest scans have emerged as a valuable tool for opportunistic CVD screening, yet existing deep learning models often fail to explicitly capture the distribution of coronary artery calcification (CAC) and cardiac fat, which are critical biomarkers in clinical diagnosis. In this work, we propose CAC-MAE, a calcification-aware masked autoencoder that leverages self-supervised pre-training on large-scale LDCT datasets to enhance CVD-related feature learning. Unlike conventional methods, CAC-MAE explicitly integrates CAC and fat segmentation as independent inputs, applying separate masking strategies to encourage a more structured feature representation. Following the pre-training of CAC-MAE, we further fine-tune the encoder with an attentional pooling layer as the output head, forming CAC-Net, a specialized model for accurate CVD risk screening from LDCT images. We validate our approach on a large-scale public dataset consisting of 33,413 LDCT images from 10,395 subjects and demonstrate that the proposed CAC-Net significantly outperforms state-of-the-art models, achieving superior classification performance in terms of area under the receiver operating characteristic (AUC) and mean average precision (mAP). By explicitly modeling clinically relevant anatomical structures, CAC-Net bridges the gap between automated deep learning and radiologist decision-making, offering a promising AI-assisted solution for CVD risk stratification in clinical practice. Source code is publicly available at https://github.com/RPIDIAL/CAC-MAE .