On October 6, 2013, Kazhdan was critically injured in a car accident while riding a bicycle in Jerusalem.

His son, Eli Kazhdan, was general director of Natan Sharansky's Yisrael BaAliyah political party (now merged with Likud).

He is known for collaboration with Israel Gelfand, Victor Kac, George Lusztig (on the Kazhdan–Lusztig conjecture on Verma modules), with Grigory Margulis (Kazhdan–Margulis theorem), with Yuval Flicker and S. J. Patterson on the representations of metaplectic groups.

He was the doctoral advisor of Vladimir Voevodsky, a recipient of the Fields Medal, one of the highest awards in mathematics.

In 2012, he was awarded the Israel Prize, the country's highest academic honor, for mathematics and computer science.