In response to queries from The Straits Times, the Ministry of National Development (MND) confirmed the probe, saying it had been alerted to the incident.
"Investigations are ongoing in respect of possible breaches by the various parties," a spokesman said, without identifying the individuals implicated.
"MND and other government agencies take a serious view of such breaches, and will not hesitate to take firm action against those who are found to have violated safe distancing measures."
Mediacorp celebrities - Xu, Shane Pow and Terence Cao - apologised on Wednesday (Dec 23) via the broadcaster after photos of them apparently breaching Covid-19 regulations were posted on social media.