The image compared the risk of Covid spread in scenarios of different mask wearing and social distancing.
But Mr Swinney, who is also Covid recovery secretary, did not include a source for the figures, and they have been labelled misleading by opposition MSPs.
The image, which has been retweeted 500 times from Mr Swinney’s post, was also shared by the SNP Largs branch and leader of Edinburgh City Council Adam McVey.
It appears to have been present on the internet for at least a year, but its origin is not clear and the Scottish Government has not yet provided a source for the information.
Mr McVey confirmed he shared the graphic without knowing its source. He said that while figures from experts are “interesting”, they don’t change the conclusion that wearing a mask reduces transmission.
The graphic states there is a 90 per cent risk of Covid transmission when two people are not social distancing or wearing masks, which drops to 20 per cent when the non-infected person puts a mask on.
This falls to 5 per cent when the infected person puts a mask on, the graphic states, and to 1.5 per cent when both are wearing masks and zero per cent when both are wearing masks and standing at a distance of two feet.
There is no information on whether the subjects are indoors or outdoors, or the type of mask used.
Some have questioned whether the view there is no risk of Covid spread at all when two people are distanced and wearing masks – whether indoors or outdoors – is correct.
Mr Swinney wrote in his post: “As we move to level zero in Scotland – marking good progress on our careful process of relaxing restrictions – this is a helpful graphic showing why we must use face coverings and keep our distance.”
The Scottish Conservatives have labelled the image “misleading”.
Scottish Conservative shadow cabinet health secretary Annie Wells said: “John Swinney should delete this misleading graphic.
“It wrongly sends a message that there is no risk from Covid in certain circumstances and makes several claims that appear to be unfounded.
“This looks unnecessarily reckless coming from a senior SNP Government minister.
“We’ve all got a duty to call out fake news and this misleading post blurs the well-intentioned message he seems to be trying to send that wearing masks can reduce the spread of the virus.
“The Covid recovery secretary needs to wise up and be more careful when sending public health messages, especially on the day that restrictions are eased across Scotland.”
Asked for the source of the graphic, Mr McVey said: "The inescapable fact is that wearing a mask reduces the spread of this virus. That’s the information that people need.
"With cases still way too high in the [Scottish] capital, it’s crucial everyone acts with caution and consideration for others, particularly as restrictions are further eased.”
A Scottish Government spokesperson said: “The science – and the DFM’s message – is clear – masks and physical distancing help prevent transmission of Covid-19, and it is important people do not undermine public health messaging by suggesting otherwise.”