The Sharks said on Tuesday that Steyn sustained acute department syndrome in his lower left leg, which is swelling, and inflammation that needs surgery to release pressure around the muscles and nerves.
Steyn had surgery in Dunedin following the Sharks' Super Rugby loss to the Highlanders last Saturday and will return home from the tour. It was originally feared he had broken his leg.
The Sharks also said Springboks prop Tendai Mtawarira would be out for three weeks with a left calf muscle tear.
South Africa's international season kicks off in a month with a four-team tournament involving Scotland, Samoa and Italy.