The Scottish Conservatives had asked the UK Statistics Authority to investigate Mr Swinney’s sharing of unverified Covid-19 transmission statistics on social media.
The Deputy First Minister shared a graphic on Monday giving details of the risk of Covid transmission in different scenarios of mask-wearing and social distancing.
The graphic claimed there was no risk when two people were both wearing masks and standing at a two metre distance.
A spokesperson for the Scottish Government later admitted Mr Swinney had shared the graphic without knowing its source.
Mr Swinney on Wednesday night deleted the graphic and issued an apology.
He posted on his Twitter account: “I shared an image on Monday to illustrate that masks and distancing can help stop Covid transmission.
"I have now deleted the image as the figures in it were not verified. Sorry for that. But the message is unchanged: masks and distancing remain critical to beating this virus.”
Deputy chief medical officer Dr Nicola Steedman was unable to confirm the information contained in it was accurate when asked during a Covid-19 briefing on Tuesday.
Mr Swinney had not acknowledged accusations the graphic’s figures are misleading until Wednesday night.
Scottish Conservative MSP Annie Wells had written to Sir Ian Diamond of the UK Statistics Authority asking him to investigate the issue and take action if needed.
She said: “The continued use of an unverified graphic like this is potentially dangerous. It undermines the serious public health message that masks can limit the spread of the virus.
"It may even convince some people that there is zero risk from Covid in certain situations, which is not supported by science.
“The repeatedly poor judgement from the SNP Government on this issue is concerning. Fake news must be stamped out and we have reported this graphic to the UK Statistics Authority for their input, since SNP ministers will not act.”
Nicola Sturgeon defended Mr Swinney on Tuesday, saying his message was that masks help to reduce Covid-19 transmission.