The characteristics of common prosperity include harmonious relationships between humans and the environment, as well as sustainable economic and social growth. The process of achieving common prosperity will necessarily have an impact on carbon emissions. In this article, panel statistics collected from 30 Chinese provinces and cities between the years 2006 and 2020 are utilized to assess the level of common prosperity and the intensity of carbon emissions in China. Then the SDM model is applied to explore the effects of the common prosperity level on the intensity of carbon emissions. The findings reveal that: (i) The common prosperity level in China has shown an increasing tendency. Between 2006 and 2020, the mean level of common prosperity increased from 0.254 to 0.486. From the regional perspective, eastern China has seen greater levels of common prosperity than central China, while central China has experienced greater levels of common prosperity than western China; regional disparities in the degree of common prosperity are substantial among Chinese provinces from 2006 to 2020; the common prosperity level is relatively high in economically developed provinces and relatively low in economically backward provinces. (ii) China's carbon emission intensity shows a continuous downward tendency. The annual average intensity of China's carbon emissions decreased from 4.458 in 2006 to 2.234 in 2020. From the regional perspective, the three main regions' carbon emission intensity likewise exhibits a decline in tendency between 2006 and 2020; still, western China continues to have the greatest carbon emission intensity, following central China, while eastern China has the smallest; however, certain provinces, notably Inner Mongolia and Shanxi, continue to have high carbon emission intensity. (iii) China's common prosperity level and carbon emission intensity both exhibit positive spatial autocorrelation at a 1% significant level under the adjacency matrix. The spatial agglomeration effect is significant, and adjacent provinces can affect each other. (iv) The SDM (Spatial Durbin Model) model test with fixed effects finds that the increase in the level of common prosperity suppresses the intensity of carbon emissions in the local area and neighboring regions. (v) The mediating effects model indicates that the process of common prosperity suppresses carbon emission intensity through high-quality economic development, narrowing the income disparity, and the development of a sharing economy.