Labour councillor Alan Dudson made the remark after he had chaired Cannock Chase District Council's virtual full council meeting earlier this month, which was broadcast live over Zoom.
The council's monitoring officer has received an official complaint over the comment but is understood to have decided to take no further action.
In the days after the meeting, council chairman Mr Dudson wrote to councillors after many of them had expressed concern regarding the conduct of some of the members in attendance.
In the letter he noted concerns over "inappropriate criticism of named councillors", allowing members the opportunity to "exercise their rights to speak", and "digital etiquette" – all issues he said had "the potential to damage the reputation of the council".
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He went on: "I also inadvertently made an inappropriate remark after the formal council meeting had finished and during an informal discussion and I wish to formally apologise to all members for this."
Mr Dudson is understood to have suggested Chinese people were to blame for spreading Covid-19. The remark was not part of the meeting broadcast to the public.
A formal complaint has been made regarding two incidents from the meeting, one of which is Mr Dudson's comment, although it is understood that that no disciplinary action will be taken against him.
The council's monitoring officer, Ian Curran, told councillors he had decided to deal with the matter internally as "it would not appear to serve the council's interest to put this allegation into the public domain".
He is said to have advised Mr Dudson that his remark was unacceptable and that any similar statements in future would see him put before the council's standards process.
Mr Dudson represents Brereton and Ravenhill and also sits on Staffordshire County Council. He is on his second stint as council chairman having previously held the role in 2017-18.
When approached by the Express & Star, Mr Dudson said: "I've got nothing to say."