"We must first give our government a chance to respond. So our press conference is postponed to tomorrow [Thursday] at 10:00," ANC spokesperson Jackson Mthembu told reporters in Johannesburg.
"We need to apply our minds adequately to the report so that we don't just come here with something that we have not applied our minds to."
He said the briefing was initially earmarked for 16:00 on Wednesday, because the ANC thought Madonsela would have completed her release of the report in Pretoria by then.
"Our plans have been messed up by the length of the report. She is still on the podium even now - that's why we decided to postpone," Mthembu said just after 16:30.
Madonsela's report found that Zuma and his family had unduly benefited from the upgrades to his private homestead in Nkandla.
Government was expected to brief media at 15:00 on Wednesday, however the briefing had not yet started by 16:45.