The comments were made at the Scottish Parliament bar to Conservatives Mary Scanlon and Alex Fergusson, before Ms Cunningham left on Wednesday evening, however after several calls for an apology, the SNP minister will now write to the pair.
An SNP spokemsman said: “Roseanna’s intention was to make light-hearted comment to a fellow SNP MSP and some Tory members as she was leaving – there was certainly no offence intended, and of course she apologises if any was taken.
“She is now writing to the Tory members concerned to make that clear and to apologise for any offence.”
The Scottish Conservatives issued a statement saying they would draw a line under the matter.
“This was an unfortunate incident,” a spokesman said.
”We are pleased Roseanna Cunningham will be making an apology to the members concerned for her comments.
”As far as we are concerned the matter is now closed.”