Magistrate Steven Whalen gave city attorney John Schapka seven days to locate two hard drives of backup data created by a city computer specialist from Kilpatrick's home computer, the Detroit Free Press reported.
Schapka was also ordered to search for CDs containing files the city downloaded from Kilpatrick's official computer before Kilpatrick's hard drive went missing, the newspaper said.
The evidence is being sought by attorney Norman Yatooma, who represents the family of Tamara Greene, a stripper who danced at a rumored but never-proved party at the mayor's mansion and was later killed in a drive-by shooting.
Greene's family sued Kilpatrick and the city, saying officials hindered her murder investigation so her killers couldn't be found.
The city and Kilpatrick have both denied the accusations.
Yatooma, who repeatedly has accused the city of concealing evidence, said he was pleased by the order.
"People accuse me of going on fishing expeditions, but sometimes, when you go fishing, you catch something," he said.