Industrialization and increased energy use are leading to a greater influence of environmental and climate challenges on human existence and progress. China’s emissions in 2023 totaled 12.6 gigatons, representing 35% of global emissions, establishing it as the top carbon emitter globally. Combined with China’s industrial structure, it is essential to investigate carbon reduction in the building sector due to its significant contribution to carbon emissions. This study introduces a third-party organization into the relationship between stakeholders, based on traditional government regulation. It constructs a three-party dynamic evolution model involving the government, environmental protection organization, and construction enterprise. The study analyzes the evolution process of the three-party strategy selection using evolutionary game theory. We analyze the elements influencing decision-making for the three parties through simulation analysis and provide appropriate recommendations. The study’s findings indicate that low-carbon construction in China’s construction sector is an intricate system involving several stakeholders, each guided by their own interests when determining their behavioral methods. Government penalties and financial subsidies can influence construction enterprises to adopt low-carbon production practices to some degree, but excessive rewards and punishments may not support system stability.