Prefabricated buildings are widely utilized due to their effectiveness in reducing carbon emissions. The construction stage has a significantly higher carbon emission rate than the other stages of their life cycle, but this is difficult to accurately quantify and predict due to the high variability. This study clarifies the system boundary of carbon emissions and the parameters of influence in carbon emissions predictions. The carbon emission quantification model was improved by using the process analysis method and the carbon emission factor method, and a modular calculation formula was proposed. Based on the machine learning algorithm, a carbon emissions prediction model for prefabricated buildings’ construction stage was established and hyperparameter optimization was conducted. A sample database for predicting prefabricated buildings’ carbon emissions during the construction stage was established using a modular quantification method, and the thin plate spline interpolation algorithm was introduced to expand this. The prediction results of carbon emission prediction models using four algorithms, SVR, BPNN, ELM, and RF, were compared and analyzed by RMSE and R². The results show that the model based on BPNN has the highest prediction accuracy when determining the carbon emissions of prefabricated building during the construction stage, and this method can provide a more accurate reference for subsequent quantitative research on carbon emissions from prefabricated buildings.