Tennis officials say no-one was injured, though the drone briefly interrupted a tennis match.
The incident took place at the Louis Armstrong Stadium on Thursday evening.
One of the players in action at the time, 26th-seed Flavia Pennetta, described hearing the drone fly by, not knowing what it was and fearing the worst.
"With everything going on in the world... I thought, `OK, it`s over.` That`s how things happen," Ms Pennetta, 33, told the Associated Press news agency.
She said they were never told by the umpire or US Open officials that the object was a drone. It reportedly broke into pieces as it landed, interrupting the match as police and fire emergency personnel investigated.
"If there had been spectators, it would have hit them and done a lot of damage," she added. The 10,000-seat stadium was only partially filled at the time, compared to several hours earlier when it was packed.
In fact it was not the first time the Italian player has had an encounter with a drone mid-match, according to New York Daily News. Another New York man was arrested during last year`s US Open for piloting a drone outside the tennis grounds while Ms Pennetta was playing Serena Williams in the quarter-finals.
Ms Pennetta later went on to win against Romanian Monica Niculescu, 27, taking her into the third round of this year`s tournament.
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