The flags were found fluttering early Tuesday from poles perched on the stone supports where two American flags are normally positioned.
The official said that the NYPD has video showing four people entering a walkway on the bridge at about 3:30 a.m., close to when the lights that normally illuminate the American flags on top of the bridge went out. One of them had what "possibly looks like a skateboard."
Police don't yet know who the young people are, and are continuing to scour surveillance video and social media in their investigation.
The bridge is one of the most heavily secured landmarks in the city, constantly monitored by surveillance cameras.
The American flags fly from above the pillars year-round and are replaced by transportation workers when they become frayed about every two months, police said. They are lit from the bottom by a lamp at the base of each tower at night.
More than 120,000 vehicles, 4,000 pedestrians and 3,100 bicyclists cross the Brooklyn Bridge every day, said the city's Department of Transportation, which maintains the crossing.