The laboratory's medical director professor Anthony Dodds blamed the mistake on the "large volume of tests" they were processing.
Those affected were notified of their result, for swabs taken from December 22 and December 23, last night at 8pm.
Professor Dodds said they had become aware of the mistake this morning.
"These people had tested positive to Covid," he said.
"As soon we became aware of the issue this morning, SydPath immediately commenced a process to contact impacted people.
"We sincerely apologise to all those impacted."