Egged on by another person, a youth sliced the canopy of the Lorong Halus red bridge, a popular attraction in Punggol.
A video on Instagram shows him using a penknife to do it while a voice could be heard saying: "Eh, cut, cut, cut some more, cut some more."
The Straits Times understands that the incident took place on Thursday.
Later the same day, the youth posted an apology on his Instagram account, admitting his stupidity in doing it and expressing the hope that he would not be charged with "vandalism to public property".
National water agency PUB, which manages the Lorong Halus Wetland where the bridge is, said yesterday it has made a police report.
The police told The Straits Times they are investigating the incident.
The video, which went viral, appears to have been deleted from the youth's Instagram account as of 6.30pm yesterday.
In the video, the youth is seen holding a penknife and crouching on the guardrail of the bridge while a person off-camera tells him to wait, before saying, "Okay, go, go, go".
He then reaches up and begins slicing a hole in the canopy as the person off-screen encourages him to "cut some more".
When done, he jumps back onto the bridge, and the video shows in the background several young people who are sitting down.
A person is heard asking the youth for his Instagram handle before the video ends.
The youth, in his apology shared on various sites, wrote: "I am sorry for what I have done today... I should have been mature enough to think about what is right and what is wrong. I admit that the thing I did was a crime as it counts as vandalism to public property.
"I hope that you guys will not take any action over my stupidity. I hope you guys won't press charges against me."
He added that "it was a childish act to look cool".
He also apologised to the "fixed community", a reference to the community of cyclists who ride fixed-wheel bicycles. Some netizens had linked him to the community as he appeared to be wearing a jacket bearing the logo of one of its groups.
In July, Instagram videos of a youth throwing bicycles from bike-sharing firms ofo and oBike off the same bridge went viral as well.
At the time, a person could be heard in the background of the videos warning the youth he might get "stomped", referring to the footage being shared on citizen journalism website Stomp.