Hoggard, who was part of the England team which won the 2005 Ashes, was one of the individuals charged by the England and Wales Cricket Board last June in a disciplinary case examining allegations of racism and bullying made by Rafiq.
The case is due to be heard in public by a Cricket Discipline Commission panel at the start of next month but Hoggard confirmed that he was withdrawing from the process, because he did not feel he would get a fair hearing.
Hoggard's former Yorkshire team-mate Andrew Gale, another of the individuals charged, announced last year he was not willing to engage with the process, which he described as "tainted".
Hoggard is understood to have been interviewed by the BBC in relation to the case.
Rafiq alleged to MPs when appearing before the Digital, Culture, Media and Sport committee in November 2021 that Hoggard had used the phrase "elephant washer" towards him, and subjected him to abuse "on a daily basis…all day, every day".
Rafiq also alleged Hoggard made players of Asian heritage sit together in the changing room. During his oral evidence, Rafiq did credit Hoggard with having made contact to apologise.
The ECB announced last June it had charged a number of individuals with improper conduct and alleged breaches of its anti-discrimination code. Yorkshire were also charged over their handling of the allegations.
Responding to Hoggard's withdrawal, and reports that two other individuals had also withdrawn, the ECB said: "Individuals are entitled to choose not to participate in the hearings if they wish, but the cases will still be heard in their absence and we are satisfied that the disciplinary process in this matter has been both rigorous and fair.
"The ECB's investigation and disciplinary process has been overseen by an independent committee and specialist leading King's Counsel (KC).
"As with any case before the Cricket Discipline Commission, defendants are entitled to a fair hearing by an independent and experienced CDC Panel where they can call witnesses, and they can also challenge the evidence in support of the charge, including through cross-examination of the ECB's witnesses. It is entirely the decision of defendants if they choose not to take advantage of this opportunity.
"At the end of the hearing it is for the independent CDC Panel, not the ECB, to determine guilt or otherwise and any sanction."