Ms Sturgeon met with Jim McColl on May 31, 2017, as concern about slippage on the contract to build two ferries at the shipyard emerged.
She was asked about this meeting when she appeared at Holyrood's public audit committee in November.
The committee is investigating the two overdue ferries at the Port Glasgow shipyard, which are years late and almost three times over budget.
During her committee appearance, Ms Sturgeon said she did not know whether a minute of the 2017 meeting had been taken, but a special adviser had been present with her.
She said Mr McColl had expressed concerns about the structure of milestone payments to the yard and the amount of money involved in a surety bond.
The public audit committee later wrote to the First Minister asking for any minutes or notes relating to the meeting.
She has already provided the committee with an email from a special adviser, which was sent just afterwards.
The email said the First Minister had asked for a briefing on the surety bond and any legal advice regarding further changes to the contracts.
In her latest correspondence with the committee, which was published on Monday, the First Minister said there was no further note of the meeting.
Ms Sturgeon said: "Officials have been unable to locate a note of this meeting over and above the document already provided.
"As I confirmed in my last letter, in compliance with the ministerial code, a special adviser was present at the meeting and actions arising were relayed to officials and clearly indicate the topics discussed.
"The committee already has that email."
The Conservatives later accused the First Minister of being in breach of the ministerial code.
MSP Graham Simpson said: "Nicola Sturgeon's admission that officials have been unable to locate a note of her meeting is a damning indictment of this Government's evasive and secretive conduct, as well as an obvious breach of the ministerial code.
"She should refer herself for investigation immediately. When huge sums of taxpayers' money are involved, the public expects and deserves complete transparency and accountability.
"This kind of response to the public audit committee is unacceptable."
The contract for the two ferries – the Glen Sannox and the as-yet unnamed Hull 802 – was awarded to Ferguson Marine while under Mr McColl's ownership.
However, it later fell into administration and was nationalised in 2019.
The correspondence was published after it was announced last month a Turkish shipyard has been named as the preferred bidder to build two new ferries for Scotland’s island communities.
Caledonian Maritime Assets Ltd (Cmal) has announced it intends to award the contract to the Cemre Marin Endustri AS shipyard in Turkey.
The new vessels will be deployed on the Uig, Tarbert and Lochmaddy routes and will be built to the same specification as the Islay ferries already under construction at the Turkish shipyard.