The Sale Sharks flanker picked up the problem during the 36-16 defeat by the Springboks in Durban last weekend.
But the 28-year-old British & Irish Lion insists he will be ready for the game in Port Elizabeth on Saturday.
White said: "I know my own body and the medics, led by physio Bob Stewart, are doing a great job. I will be 100 per cent on Saturday."
Openside flanker Donnie Macfadyen, who injured a chest-bone at the ABSA Stadium, is also expected to be available for Scotland head coach Frank Hadden.
But Glasgow Warriors number eight John Beattie has picked up a stomach virus and did not train with the squad on Tuesday.
Full-back Hugo Southwell and winger Sean Lamont are recovering well from shoulder and leg injuries respectively.
Hadden said: "Sean is better than expected. We felt there was no chance of him playing in the second Test earlier in the week.
"There is a glimmer of hope there now. We will be monitoring him over the next 24 hours."