Burger, capped 68 times, injured his knee at the end of February but there has been no progress in his rehabilitation according to Allister Coetzee, coach of his club Stormers.
"The position with Schalk is very frustrating and we are going to get a full assessment shortly from a physician on where it should be taken from here but you can take it as read that we won't see Schalk play before the end of this season," Coetzee said.
"Without even looking at the physician's report, we are writing him off for the year."
Pietersen, a 26-year-old veteran of 45 tests, suffered a fracture of the thumb during the weekend's Super Rugby final and will undergo surgery on Wednesday.
Springbok coach Heyneke Meyer has recalled Stormers centre Juan de Jongh, a 2011 World Cup player and a controversial omission from the original squad, in Pietersen's place.
The 24-year-old De Jongh made his Springbok debut against Wales in 2010 and has 10 test caps.
"We decided to pick Juan as he provides midfield cover, an area where we are perhaps a bit thin now that JP is out," Meyer said in a statement on Monday.
"Losing JP is obviously a massive blow as he's been playing some superb rugby lately, but Juan has also been in good form for the Stormers and was one of the unlucky players to miss out on initial selection.
The Rugby Championship replaces the Tri-Nations this year with Argentina joining the existing line-up of South Africa, Australia and New Zealand. South Africa finished last in last year's Tri-Nations, with just one win in four matches.