Yu fled the assailants and ran into incoming traffic, police said. He was pronounced dead at a nearby hospital. The driver of the car was not charged.
The 13-year-old, whose name was not released because he is a minor, was in custody on the second-degree manslaughter charge, police said.
Yu, a Ph.D. candidate in statistics and a teaching fellow in the Graduate School of Arts and Sciences, was a native of China.
"He's a really nice guy, and he's worried about others," said Chao Sun, 24, who said she had been dating Yu for several months. "I can't imagine he would do anything to harm other people."
In an e-mail sent to students and faculty, Columbia University President Lee C. Bollinger informed them of Yu's death.
"As a community we mourn the loss of one of our members, and especially of a young person with much to look forward to in a life of promise," Bollinger wrote.
