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Zhu studied mathematics at Peking University, graduating in 1984. He was part of the second cohort of students to be awarded the Shiing-Shen Chern scholarship, established to support outstanding Chinese students in pursuing further studies in the US. The scholarship was set up by mathematician Shiing-Shen Chern in collaboration with the American Mathematical Society.
In 1990, Zhu obtained a doctorate in mathematics from Yale University, where he studied under mentor Igor Frenkel.
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Zhu was a division research fellow at the California Institute of Technology (Caltech) from 1990 to 1993, then held visiting positions at the Institute for Advanced Study at Princeton University and the Max Planck Institute in Bonn.