The virus is not ransomware and there is no data breach, says a city spokesman, but any court motion or documents must be filed in person and can't be filed on the court's e-file system.
Emails for judicial employees, including judges and court staff, have also been shutdown as the city's IT department works to fix the problem.
Authorities are also looking into the origin of the virus.
Any scheduled hearings have gone on as scheduled.
A spokesman for the District Attorney's office says all work is being backed up electronically and with paper filings as they work to fix the problem.
Traffic court was not affected.