The school made the announcement Wednesday ... saying both Saban and athletic director Greg Byrne had tested positive and are immediately headed for quarantine.

Saban said in a statement he is displaying no symptoms as of this moment ... and is undergoing further tests to make sure his results were NOT a false-positive.

"I found out earlier this afternoon that I had tested positive for COVID-19," 68-year-old Saban said.

"I immediately left work and isolated at home. At this time, I do not have any symptoms relative to COVID, and I have taken another PCR test to confirm my diagnosis."

"I informed our team of my positive test at 2 p.m. today on a Zoom call and let them know offensive coordinator Steve Sarkisian will oversee preparations at the complex while I work from home."

Byrne also issued a statement saying, "We've been diligent about mask wearing and social distancing from the start and want to continue to encourage you all to take the necessary precautions to help stop the spread of this virus for yourself and those around you."

Of course, aside from the virus' potential effects on the two 'Bama employees ... the tests could have a drastic impact on the Tide's 2020 season.

Georgia is 3-0 and is widely considered Alabama's biggest threat to an SEC crown this season ... and playing the Bulldogs without Saban on the sidelines won't make getting a W any easier.