A Scottish Government spokeswoman said: “Mr Yousaf has given a given a formal, in-person apology to the Chamber of the Scottish Parliament and to the Presiding Officer.
“As such we consider the matter closed.”
Humza Yousaf announced on Tuesday plans for the Scottish Fire and Rescue Service and more than 100 military personnel to support the ambulance service – which is currently under acute pressure, causing severe waits for patients.
But details of the announcement appeared in the Daily Record hours before the statement was made.
The ministerial code states that announcement should be made to parliament when Holyrood is in session.
Mr Yousaf was rebuked by Presiding Officer Alison Johnstone ahead of Tuesday’s statement, who said if it happened again she would not allow the statement to be made to MSPs and would instead move straight to opposition questions.
He subsequently apologised to Ms Johnstone and the parliament.
Scottish Tory chief whip Stephen Kerr wrote to First Minister Nicola Sturgeon, urging her to step in, which she has now said she will not do.
“Yesterday, in his statement to Scottish Parliament, it was confirmed by the Cabinet Secretary for Health and Social Care that he leaked the content of his statement to the Daily Record ahead of delivery to parliament,” he said.
“This included multiple important announcements of government policy on tackling the current ambulance crisis.”