Opposition politicians and some Labour sources have called into question Mr Matheson's judgment and credibility following the incident in a Glasgow car park, which saw him and an unnamed 38-year-old man reported for alleged indecency.
Mr Matheson, 48, admitted to having an affair and cheating on civil partner Stephen Wallace with a man described as a former lover, saying he had not lived up to his own standards.
Yesterday, the council leader was back behind his desk at Glasgow City Chambers. The procurator-fiscal has decided no further action will be taken after concluding there was insufficient evidence that a crime had been committed.
However, on the back of the debacle over the delays and potential scrapping of the £15 million George Square revamp designs, even internal party sources said the incident would continue to overshadow Mr Matheson's leadership.
The SNP used the incident to call into question decisions over which Mr Matheson's leadership has presided, but The Herald understands there is no appetite within the council's Labour administration to oust the leader.
One Labour source said: "Gordon Matheson may have the support of [Scottish Labour leader] Johann Lamont and [shadow Secretary of State for Scotland] Margaret Curran, but privately senior people in the party will be horrified at this.
"He may tough it out and limp on, but this isn't going away for a long time.
"People have been suspended in the Labour group in the city council for less than this."
Another said: "Had this been an election year this could have seriously damaged Labour in Glasgow. There's a lot of social conservatism in the party's heartlands and this won't play well. Labour's closed ranks here but privately a lot of people asking what kind of judgment puts everything at risk for cheap sex in a car?"
Police were informed on December 12 that a passer-by had encountered two men behaving in an inappropriate manner at Linn Park in Cathcart on the city's south side.
Mr Matheson and the other man were spoken to by the police, who then reported them to the procurator-fiscal.
News of the incident broke just as it emerged that the judging panel in the George Square design competition, a personal project of the council leader, were unlikely to pick any of the shortlist of six.
Tory councillor David Meikle said: "Just like the George Square fiasco, this incident shows a total lack of judgment.
"It's now up to Labour to take action as we've seen them do with other councillors. A sex act in public is considerably more serious than what some have been suspended for."
Last night, the SNP said it had no wish to comment on Mr Matheson's private life. A spokesman added: "The issues which are important to the City are Labour's scandalous £500,000 pay-off to a supposed anti-poverty boss, which has been condemned by the Charity Regulator; the closure of day centres for adults with learning disabilities without proper consultation, and their incompetence over plans to redevelop George Square."
Labour's group whip on the council, Alastair Watson, refused to say whether Mr Matheson would even be given a warning.
He said: "This is a private matter and a tragic personal issue for Gordon Matheson. He now needs time and space to get his life in order and sort this out with his partner."
The Labour Party was approached for a comment, but had not responded last night.