Generative artificial intelligence (Gen AI), represented by ChatGPT, is lowering the cost of knowledge acquisition and integration. While providing intelligent support for cultivating university students’ innovation ability, it also brings risks such as a weakened willingness to explore independently, impaired critical thinking, and a diluted sense of responsibility. Taking the constituent dimensions of university students’ innovation ability as an analytical framework, this paper examines the empowering opportunities and weakening effects of Gen AI. Cultivating university students’ innovation ability in the context of generative AI is both a contemporary issue that technological change poses for higher education and an educational requirement of the mission of fostering virtue through education in universities in the new era. To this end, coordinated efforts should be advanced at the three levels of content, practice, and institution: reshaping the content and methods of innovation ability cultivation in universities, emphasizing the building of human-machine collaborative platforms and practical components, and improving the support mechanism for cultivating university students’ innovation ability, so as to stimulate university students’ motivation to innovate and sense of responsibility, and make technology serve their growth and talent development.