The documents contained confidential information, including detectives' Social Security numbers, bank information and unveiled undercover officers' identities, WPIX-TV, New York, reported.
Ethan Finkelstein said he was watching the parade at 65th Street and Central Park West, when he and a friend noticed a strip of confetti stuck onto her coat.
"It landed on her shoulder," Finkelstein said, "and it says 'SSN' and it's written like a Social Security number, and we're like, 'That's really bizarre.'"
Finkelstein, a Tufts University freshman, said he and his friends were concerned and picked up more confetti that had fallen around them.
"There are phone numbers, addresses, more Social Security numbers, license plate numbers and then we find all these incident reports from police."
The documents were apparently from the Nassau County Police Department.
"I'm just completely in shock," said Finkelstein, 18. "How could someone have this kind of information, and how could it be distributed at the Thanksgiving Day Parade?"
Nassau County Police Department Inspector Kenneth Lack said in a statement the department "is very concerned about this situation."
"We will be conducting an investigation into this matter as well as reviewing our procedures for the disposing of sensitive documents," he said.
Meanwhile, parade sponsor Macy's said it uses "commercially manufactured, multicolor confetti, not shredded paper," so it is unclear where the shredded documents came from.