Gibbs scored just eight runs in total in the first Test at Centurion, a game South Africa won by 128 runs.
"Herschelle and I had a meeting on Friday, and we agreed that a break and a fresh start next season will do him a world of good," said Haroon Lorgat, the convenor of national selectors.
"He has therefore been released from the squads for the final two tests against New Zealand.
"Garnett is most unfortunate to have picked up a shoulder strain when he was set to play in the first Test at Centurion.
"With the outstanding performances of Makhaya Ntini and Dale Steyn in this match, and with Andre Nel in reserve, we have decided to release him."
The 32-year-old Gibbs has played 76 Tests, scoring 5,591 runs at an average of 45.45.
The second Test starts at Newlands on April 27 with the third and final Test at the Wanderers from May 5.
South Africa squad:
Graeme Smith (capt), Jacques Kallis, Boeta Dippenaar, Ashwell Prince, AB de Villiers, Mark Boucher, Shaun Pollock, Nicky Boje, Andre Nel, Makhaya Ntini, Dale Steyn, Andrew Hall, Jacques Rudolph, Hashim Amla.