"Further news on the extent of his injury and the rehabilitation process will be made in time," his club side the Sharks said on their website (www.sharksrugby.co.za) on Monday.
Steyn could miss three test matches next month, starting with the one against Italy in Durban on June 8.
A week later the Springboks tackle Scotland in Nelspruit and they will then meet one of those two teams or Samoa in a four-nation tournament decider in Pretoria on June 22.
According to media reports, Steyn underwent emergency surgery on Sunday to alleviate pressure on his leg after receiving a heavy blow as the Sharks lost 25-22 to the Highlanders in Dunedin.
Although x-rays showed no fracture, the centre was said to be in excruciating pain.
The reports added Steyn would need further surgery on Tuesday but that he may be well enough to fly home on Thursday.
The centre returned to South Africa midway through last year following a two and a half year stint in France with Racing Metro 92.
- Sports & Recreation