Neural View Synthesis (NVS), such as NeRF and 3D Gaussian Splatting, effectively creates photorealistic scenes from sparse viewpoints, typically evaluated by quality assessment methods like PSNR, SSIM, and LPIPS. However, these full-reference methods, which compare synthesized views to reference views, may not fully capture the perceptual quality of neurally synthesized scenes (NSS), particularly due to the limited availability of dense reference views. Furthermore, the challenges in acquiring human perceptual labels hinder the creation of extensive labeled datasets, risking model overfitting and reduced generalizability. To address these issues, we propose NVS-SQA, a NSS quality assessment method to learn no-reference quality representations through self-supervision without reliance on human labels. Traditional self-supervised learning predominantly relies on the "same instance, similar representation" assumption and extensive datasets. However, given that these conditions do not apply in NSS quality assessment, we employ heuristic cues and quality scores as learning objectives, along with a specialized contrastive pair preparation process to improve the effectiveness and efficiency of learning. The results show that NVS-SQA outperforms 17 no-reference methods by a large margin (i.e., on average 109.5% in SRCC, 98.6% in PLCC, and 91.5% in KRCC over the second best) and even exceeds 16 full-reference methods across all evaluation metrics (i.e., 22.9% in SRCC, 19.1% in PLCC, and 18.6% in KRCC over the second best).