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Byrnes was banned by a judiciary officer who found him guilty of dangerous play in making contact with Waratahs centre Tom Carter's eye area during the teams' round two clash on March 2.
But the three-man appeals committee chaired by Nicholas Davidson has found there was insufficient proof to sustain the charge.
"This was a serious allegation and must be clearly established on the balance of probabilities," said SANZAR in a statement.
The appeals committee said its examination of the evidence included extensive "but inconclusive" video footage from the match.
"Applying the standard of proof required under the rules, the appeal committee concluded that it could not be said that a breach of the laws occurred to the requisite standard as an act of recklessness which involved contact with the eye area.
"In the circumstances, the appeal was allowed and the sanction was set aside."
The initial judiciary hearing rejected the notion that Byrnes' action was eye-gouging or constituted an intentional attack.
But he was deemed to have acted dangerously in applying a headlock to Carter, which involved recklessness in making contact with the eye area.
The appeals committee first dismissed a submission by the Rebels that the judicial officer was wrong to amend detail of the citing which originally alleged an attack to the eyes as the players were getting up after clearing out.
Tully considered video footage before the players fell to ground, not as they were getting up, and that founded his decision to impose the ban.
The committee said there was no unfairness in the process adopted.
