The correspondence, signed by the DUP leader, was sent in September 2015 to former Scottish minister Marco Biagi.
The existence of the letter was first revealed when Biagi claimed on Twitter last week that Mrs Foster had once written to him asking Holyrood to curtail same-sex marriage access for Northern Ireland couples.
In a tweet, he added: “I said no. Specifically this was couples with prior Northern Irish civil partnerships, who couldn’t switch for marriages in NI (or England and Wales).”
He continued: “England and Wales still only convert their own civil partnerships. Scotland converts anyone’s.”
But when asked about the letter, the Northern Irish First Minister denied sending it.
She told BBC Radio Ulster’s Inside Politics programme last week: “I’m not quite sure what he was referring to but it certainly wasn’t a letter from me and I have no recollection of a letter from me.
“If I had written to him officially as minister of finance or something like that around recognition laws here in Northern Ireland, I have no recollection of it. I certainly didn’t write in a personal capacity.”
The letter, which was published today following a Freedom of Information (FOI) request, was a follow-up to a letter from her predecessor as finance minister, the DUP’s Simon Hamilton. Mr Hamilton’s letter has also been made public.
The letters did not cite moral or political objections to the proposed legislation in Scotland, but highlighted potential legal issues.
They said complications could arise from couples having “dual status”, where they are recognised as civil partners in Northern Ireland but as married in Scotland.
Mrs Foster wrote: “I’m sure neither of us would wish to place same sex couple in an uncertain legal position, which maybe difficult and expensive to resolve.”
Mr Biagi rejected the request from the Northern Ireland ministers.
In his reply to Mrs Foster, dated November 24 2015, he said it would “not be appropriate” to exclude Northern Ireland couples from availing of the legislation.
Stormont’s department of finance has responsibility for marriage regulations in Northern Ireland.