While artificial intelligence (AI) is being increasingly utilized in the design of museum cultural and creative products (MCCPs), limited research has explored consumer satisfaction with these AI-generated designs. This study quantitatively examined the impact of AI-generated MCCP design on consumer satisfaction and proposed strategies for improvement. A comprehensive evaluation system consisting of fourteen factor indicators across four dimensions was constructed through literature research, user interviews, and expert suggestions. On this basis, a survey with 297 consumers was then conducted using AI-generated cultural and creative products from the Dunhuang Museum. Additionally, the Importance–Performance Analysis (IPA) method was employed to analyze the importance of various factors in these AI-generated designs and their impacts on consumer satisfaction. The findings revealed that, while consumers expressed high satisfaction in terms of product functionality and creative attraction, improvements are needed in cultural expression and user experience. It is recommended that creating a multimodal museum database, developing structured prompt card models, and building an MCCP design platform with full-process AI participation would help to increase consumer satisfaction. This study can provide theoretical and practical references for the intelligent development of MCCPs’ design and promote the sustainable development of cultural heritage.