The body was found inside a wall, in a space for wires running from one floor to the next, in a university lab building where Ms. Le was last seen on surveillance camera.
The find is the latest development in a case that has gripped the Yale community for the past week. Le, a Vietnamese-American doctoral student in pharmacology, disappeared just five days before she was due to get married.
The New York Times said that the body was found just hours after her scheduled wedding.
While the remains have yet to be officially identified, Peter Reichard, the assistant New Haven police chief, said the authorities were assuming that they belonged to Ms. Le, a slight, smiling, California-bred daughter of Vietnamese immigrants, who was studying pharmacology.
The discovery ended the six-day search for Ms. Le that had begun with speculation of a runaway bride but quickly gave way to near certainty that a crime had been committed.
Le was last seen on surveillance camera tape, entering a lab building at Yale's medical school complex.
The Associated Press reported that no videotape could be found of Le leaving the building, despite the presence of 75 cameras. The body was found around 5 p.m. Sunday, AP reported.
On Saturday, the New York Daily News reported that police had questioned an unidentified Yale professor in connection with the case. The professor caught cops' attention because Le was the professor's student, and was due to attend the class on the day she vanished.
But the class was abruptly canceled - and hours later, Le was discovered missing.
The sudden cancellation near the time when Le is believed to have disappeared aroused suspicions among law enforcement, a New Haven police source said.
It was unclear what class was canceled or if the professor is a suspect. Yale officials would not comment, and a police spokesperson did not return calls.
The New York Daily News also reported that Le had penned an article on campus safety for a Yale university publication.