South African Van der Burgh won gold in the 100m breaststroke at the 2012 London Olympics and silver in Rio four years later before retiring in 2018.
He said that while the most severe symptoms from the virus had passed he was still exhausted by any physical activity.
“I have been struggling with COVID-19 for 14 days today,” he said on Twitter.
“By far the worst virus I have ever endured despite being a healthy individual with strong lungs (no smoking/sport), living a healthy lifestyle and being young (least at-risk demographic).
Although the most severe symptoms (extreme fever) have eased, I am still struggling with serious fatigue and a residual cough that I can’t shake. Any physical activity like walking leaves me exhausted for hours.
More than 14,600 people have died globally since the coronavirus outbreak began.