Building integrated photovoltaics (BIPV) contributes to promoting green and low-carbon transformation in rural areas. In order to better guide rural households to invest in BIPV projects and promote the goal of “carbon neutrality” in China’s building sector, this study integrates the theory of planned behavior (TPB), the social cognitive theory (SCT), and the PEST analysis framework. It constructs a theoretical model from the perspective of “External Factors-Internal Psychology-Investment Intention” to investigate rural households’ investment intentions toward BIPV projects and their influencing factors. Basic data were collected from 488 valid questionnaires from rural households in Henan Province, and the theoretical model was empirically tested using structural equation modeling. The results show that the model constructed from both internal and external factors effectively explains rural households’ investment intentions (II) toward BIPV projects (R2 = 0.89), with investment attitude (IA) being the strongest psychological motivation leading to their II. All four external factors—policy, economic, social, and technological—positively influence II with diminishing effects. Additionally, the policy factor has the most significant effect on IA, while the economic factor has a more prominent effect on perceived behavioral control (PBC), and the technological factor has a relatively weaker effect on the two psychological factors. Furthermore, the four external factors indirectly influence investment intentions through the two psychological factors of IA and PBC, with the mediating effect of IA being higher than PBC. Based on the findings, this study proposes effective suggestions to enhance rural households’ investment intentions toward BIPV projects.