Police said children fled from the park in Dover Street, off the Shankill Road, on Thursday and reported that a man was brandishing a shotgun.
The man is then understood to have fired a shot into the air, before leaving with a woman.
Police praised the actions of residents who, they said, stopped two people in nearby Beverley Street.
It is understood local people detained the man awaiting the arrival of police.
Chief Inspector Gavin Kirkpatrick said: “Two people are now in custody and a firearm has been recovered.
“We are at a very early stage in this investigation but at this point I’d like to give credit and thanks to the local people who intervened.
“Their prompt actions in detaining the suspects, disarming them and alerting police allowed us to make swift and effective arrests and seize the firearm for investigation.”
Neither of the two people arrested are believed to be local residents.
Police say there is nothing to suggest the incident is sectarian at this stage.