George Osborne has written to the regulator outlining his concerns.
An investigation into 30 million old life insurance policies was leaked early last Friday – prompting millions to be wiped off leading firms' shares.
It was due to be announced in the annual business plan on Monday but was leaked in the press before the weekend instead.
Mr Osborne said: "These events go to the heart of the FCA's responsibility for the integrity and good order of the UK's financial markets, and have been damaging both to the FCA as an institution and to the UK's reputation for regulatory stability and competence."
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He has put a series of questions to the FCA addressing why the leak happened in the first place and how it was handled subsequently.
Treasury Committee chairman Andrew Tyrie MP called the FCA's handling of information about the probe "an extraordinary blunder."
I would like to assure you that at the meeting last Friday, the Board of the FCA shared similar concerns to your own about the events themselves as well as the potential impact on the FCA's and UK's reputation in financial services.
John Griffith-Jones, the FCA chairman, has responded to Mr Osborne in a letter.
He wrote: "As we announced last week, we intend to do everything possible to address that harm by setting up an independent inquiry.
"I am determined to understand the FCA's role in the events of Thursday and Friday. I am already in discussion with your officials on the arrangements and terms of reference for the review, which will be done by an external legal firm and will be independent of the Executive.
"We will ensure that all the issues raised in your letter are reflected in the terms of reference of the inquiry."