The E-ACT academy group says it will replace them with "academy ambassadorial advisory bodies".
These new bodies will "play a central role in celebrating the academy's achievements", E-ACT has told its school governors in a letter.
But governing bodies, with parental representatives, will no longer hold their local schools to account.
The academy chain says it was about providing the "best possible education".
A school governor described it as "authoritarian" and "repugnant".
E-ACT's 23 schools are spread across England, with clusters in the West Midlands, Buckinghamshire, Bristol and the north west.
As an academy chain it receives public funding to operate schools, with accounts for the academic year ending in August 2014 showing an income of Â£135m.
A letter sent to governors tells them that the academy chain has decided to change its form of governance.
Instead of local school governing bodies, there will be a centralised process for monitoring standards.
The letter to governors says the academy chain would contact governing bodies "to discuss an appropriate transition date" and the replacement bodies would provide a different type of function, such as an "interface with the community".
And it invites current governors to move over to the new bodies, but these would no longer be involved in areas such as hiring senior staff and monitoring budgets and standards.
A governor in one of E-ACT's schools in the midlands said he was "shocked" at how governing bodies had been disbanded, which he described as "offensive and disrespectful to the people who freely volunteer their time to act as governors".
What makes this more controversial is that E-ACT itself has a troubled record.
In 2014, the academy chain lost control of 10 of its schools after Ofsted inspectors raised serious concerns about their performance.
Until July 2015, the chain was operating under a financial notice to improve, imposed by the Education Funding Agency.
A spokeswoman for E-ACT said the academy group had introduced "fundamental changes to how the organisation operates to ensure that every young person received the best possible education with us".
She added: "Part of this involves adopting a new governance model, in line with the Department for Education's guidance.
"We appreciate that change can be challenging for some, but we are committed to continuing to work closely with our governors and are encouraging each of them to take up posts in the newly-formed advisory bodies."
An academy chain is scrapping the current form of governing bodies for its schools in England.