Burger had an operation to repair torn ligaments in his right knee a month ago, and this week he started running for the first time.
At his current rate of recovery, Burger is set to be back in action against Italy on June 21.
"I'm feeling fine," Burger told www.superrugby.co.za. "I just can't wait to get back."
Hookers Schalk Brits and JP Pietersen have also resumed training with the squad.