The 31-year-old was injured in last week's 40-33 victory over the New South Wales Waratahs in Sydney when a team mate fell on his head during a tackle.
Blues coach Tana Umaga said in a statement that Williams was improving but they felt it prudent to rest him for the game at Eden Park, with TJ Faine coming in to replace him against the South African side.
Williams and All Blacks hooker Dane Coles are both battling concussion six weeks before the first test against the Lions on June 24 at Eden Park.
Coles has not played since March 18 after suffering knee and calf injuries before being diagnosed with concussion as well.
All Blacks captain Kieran Read and Liam Squire have suffered broken thumbs in the last two weeks and are not due back until just before the test series.
Fellow loose forward Jerome Kaino has undergone knee surgery and is not expected to return until the Lions arrive in New Zealand.
There was some good news for Umaga and the national team, however, with lock Patrick Tuipulotu cleared to play against the Cheetahs after being sidelined with a back injury since April 1.
(Reporting by Greg Stutchbury in Wellington; Editing by Peter Rutherford)
