The United Federation of Teachers says the teacher ratings are based on unproven methodology.
Union President Michael Mulgrew said the reports are also full of errors such as teachers being assessed for students they didn't teach.
The city Department of Education had planned to release the teacher ratings after news organizations filed Freedom of Information Law requests.
But the union went to Manhattan State Supreme Court on Thursday to seek an injunction preventing the release of the data.
Late Thursday, the DOE agreed to the delay.
A meeting will be held tomorrow between lawyers for the city and UFT to determine whether they will release the grades only with the teacher's names redacted.
"Today we agreed to delay the release of this data until the scheduled court hearing on November 24th. We continue to believe that it is our obligation, under the law, to provide this data, but will await the court's ruling after a full briefing."