White House press secretary Josh Earnest, who is in New Delhi travelling with US President Barack Obama, said he did not have details about the size or type of the drone, but he said the Secret Service was investigating.
Obama and first lady Michelle are on a three-day visit to India, but their daughters, Malia and Sasha, are in Washington.
The report of a drone came at a time when other threats to the President's family or their home have led to concerns about security, the New York Times reported.
The Secret Service has received heavy criticism for a number of recent security breaches, including an intruder climbing the White House fence last year and reaching the interior of the building before being caught by agents.
In October, a 23-year-old man climbed over the White House fence and was quickly arrested as he fought two Secret Service dogs.
These incidents preceded the disclosure of other serious breaches in security for President Obama and ultimately led to Julia Pierson's resignation as director of the Secret Service after 18 months on the job.