The full-back has been replaced in the 26-man squad for the Tri-Nations match against the Springboks in Cape Town by utility back Isaia Toeava.
"Isaia is currently at full-back for Auckland and has played there previously at the international and the Super 14 level," said All Blacks coach Graham Henry.
"He's also got the ability to play elsewhere in the backline which is helpful when we are a long way from home.
"Leon is improving, but the medical advice is to take things slowly," Henry added.
"He'll gradually get back into exercise and then training and then may look to play an Air New Zealand Cup match (for Canterbury)."
Wing Rudi Wulf, who is back training after suffering a knee sprain while playing for North Harbour last Friday, will also not be making the trip to Cape Town as the All Blacks coaches have opted to take three half-backs (Jimmy Cowan, Andy Ellis and Piri Weepu) instead.