The panel found the charge against Vaughan was not proved, after the case against him and five other former Yorkshire players was heard in London this month.
Yorkshire and a number of individuals were charged by the England & Wales Cricket Board (ECB) last year after an investigation into racism allegations made by Rafiq, who said in 2021 he had been a victim of institutional racism at the club.
Rafiq, a player of Pakistani descent who has said English cricket is institutionally racist, alleged Vaughan told him and other players of Asian origin that there were "too many of you lot, we need to do something about it" before a match in 2009. Vaughan strongly denied the allegation.
The CDC said its panel "was not satisfied on the balance of probabilities" that Vaughan said the words "at the time and in the specific circumstances alleged".
The panel added its findings "do not in any way undermine the wider assertions" made by Rafiq.
Vaughan, who played for Yorkshire between 1993 and 2009, was one of seven individuals charged by the ECB with using racist or discriminatory language. He was the only defendant who participated in the CDC hearing.
"It has been both difficult and upsetting to hear about the painful experiences which Azeem described over the past three years," Vaughan said in a statement on social media before the ruling was published.
"The dismissal of the specific charge that concerned me takes nothing away from Azeem's own lived experiences... I have never wanted to do anything that runs contrary to genuine efforts to clean up the game of cricket.
"I truly hope people can understand why, on a personal level, I could not just accept, or apologise for, something which I know I did not do... At times, this process has brought me to the brink of falling out of love with cricket."
The panel upheld some charges against former Yorkshire players Tim Bresnan, John Blain, Matthew Hoggard, Andrew Gale and Richard Pyrah, all of whom withdrew from the proceedings.
They were found liable for a breach of an ECB directive related to "conduct which is improper or which may be prejudicial to the interests of cricket or which may bring the ECB, the game of cricket or any cricketer into disrepute".
"Given the nature of these cases, they have taken a clear toll on everyone involved," ECB chair Richard Thompson said.
"There now needs to be a time of reconciliation where, as a game, we can collectively learn and heal the wounds and ensure that nothing like this can ever happen again."
Rafiq told Sky Sports he disagreed with the finding in regards to Vaughan but felt vindicated that all but one charge had been upheld.
"I don't want to get hung up on one individual. I think this is a wider issue," he said.
"It's been challenging for everyone concerned but if there's going to be any good out of it, people have got to really take stock, reflect, learn and the game has got to get better."
Thompson said the independent panel will determine what sanctions are appropriate where charges have been admitted or upheld.
Yorkshire and former player Gary Ballance were not required to attend the hearing after accepting their charges. The racism scandal rocked English cricket and led to numerous changes in coaching and administrative personnel at the club.
Yorkshire have admitted documents and data relating to allegations of racism were deleted or lost during the tenure of a previous regime.