The World Rugby Judiciary Committee decided not to include the All Blacks match on August 11 - a warm-up game of 40 minutes each against two county sides - in the four-week suspension given to Williams.
The 31-year-old received a red card in the second Test against the touring British & Irish Lions for a hit on Lions wing Anthony Watson, but it was initially hoped Williams' four-week suspension would be served in time for the August 19 Test in Sydney.
But a World Rugby panel, compromising three Australians, deemed the All Blacks hit-out against Manukau and Taranaki one week before the first Bledisloe Cup clash was not worthy of a "match".
Unless the decision is overturned, Williams will miss the all-important Investec Rugby Championship opener.
In a statement, NZ Rugby said: "New Zealand Rugby has confirmed that Sonny Bill Williams has appealed the World Rugby judicial committee's decision not to include the All Blacks match on 11 August in the four-week suspension given to Williams following a hearing into the red card he received in the second Test against the touring British & Irish Lions.
"As the matter will now be decided by an appeal committee, no further comment will be made at this time."