The 15-year-old girl had accompanied her father to the hospital and the incident took place when he left her in the waiting hall of the hospital to get the doctor's appointment.
The girl's father approached the police on Saturday night after which an FIR was registered.
The accused, Mohd Zafar, was arrested within hours, police said, adding, they suspect that the accused has also abused other girls who came to the hospital for treatment.
"The girl was alone in the waiting hall during evening hours. The accused took her to a room on pretext of getting her examined by a doctor and assaulted her there," a police official said.
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"When he returned to the waiting hall, he found her lying on the floor weeping. She kept repeating that she wanted to leave. On prodding a little more, she told him that the accused forced her to sit on his lap, and then touched her inappropriately. He also threatened her with dire consequences if she told anyone about it," the official said.
The girl's father approached the nearest police post at LNJP Hospital and narrated the incident to the duty officers.
Police identified Zafar through CCTV footage of the hospital and nabbed him in the early hours yesterday from a friend's house after electronically tracking his location.
During interrogation, Zafar broke down and confessed to the crime, police said, adding, he was produced before the magistrate and sent to Tihar Jail on judicial custody.
Besides investigating if Zafar abused other patients, police said it will also go through his mobile phone to check if he had filmed the child.
A medical examination of the girl confirmed the assault.