Vaughan had been suspended by the BBC in November 2021 after being implicated in Azeem Rafiq allegations of racism at Yorkshire CC.
The 47-year-old returned to the BBC's coverage for England's three-Test series against New Zealand, but staff "raised concerns" about his comeback.
Yorkshire and "a number of individuals" were charged by the ECB following an investigation into allegations of historic racism, though Vaughan was not charged and categorically denied all allegations.
On Tuesday evening, Vaughan posted a statement on his Twitter account explaining why he felt it best to temporarily remove himself from the spotlight.
Vaughan said: "On numerous occasions, I have put on record my views on the issues concerning YCCC.
"It is always regrettable when commentary on matters off the field take the focus away from what's happening on the field.
"In view of the ongoing dialogue on the subject, I have taken the decision to step back from my work with the BBC for the time being.
"The key driver for this is my concern for the wellbeing of my family members and my wish to protect their family life.
"Stepping back temporarily is also in the interests of the game and I hope that it will minimise any difficulties for my work colleagues."
Following Vaughan's announcement, the BBC said in a statement: "Following conversations with Michael Vaughan we have accepted his decision to step away from our cricket coverage.
"This is a decision we respect and understand. Michael remains under contract to the BBC."