Police closed down Botanic Gardens in the south of the city after hundreds of young people had gathered on Wednesday.
Prior to the police intervention, there had been a party atmosphere with groups drinking, playing music and playing ball games.
There are currently tight restrictions on public gatherings in Northern Ireland under Covid-19 regulations.
PSNI assistant chief constable Alan Todd said officers took “operational action” at the location.
Officers present in the park formed a line and walked across it, funnelling those gathered towards the exits.
An announcement was made that the park was being closed to ensure adherence to coronavirus regulations.
Mr Todd said a number of people had been turned away from beauty spots but that the majority had heeded the public health messages.
The traditional St Patrick’s Day celebrations, including a large parade in Belfast city centre, have been cancelled due to the pandemic.
Mr Todd previously warned that those caught breaking the rules against gathering in groups could expect to face stiff fines.
And he said people who had been fined before risked even tougher penalties.
Joining a patrol in Downpatrick, a town with historic links to St Patrick, PSNI chief constable Simon Byrne thanked the public, the vast majority of whom, he said, were adhering to the coronavirus restrictions.
“I think most people see St Patrick’s Day as a day to come together with others and we are concerned that particularly in some of the places where we would see crowds gathering, that people would do that again this year,” she told the BBC.
“We are sending out a very strong message, that people should of course mark St Patrick’s Day but they should do it in a way that doesn’t cause problems later on in the month. So they should do it with their family, inside their own bubble and really to have thought to those people who haven’t been able to access care in our hospitals because they have had to deal with the pandemic.
“So please give some thought to what you are doing today.
“We know it is yet again another sacrifice for people but we’re asking you to stay with us because we are now moving into relaxations. I think people should take optimism from that, however we need people to stay apart today.”
Mrs Foster also defended the Stormont Executive’s cautious approach to exiting lockdown.
“We are in a five-party executive; from my perspective we would like to move in a more steady way, others are more cautious,” she said.
“However, I do think it is very important that we do need to protect all of our services in our healthcare – and the best way to protect all of our services and our healthcare system is to make sure that we don’t see another rise in Covid cases.”
No further deaths of patients who previously tested positive for Covid-19 were reported in Northern Ireland on Tuesday.
But another 161 confirmed cases of the virus were recorded by the Department of Health in the last 24-hour reporting period.