The man was arrested on Sunday after the child's parents registered a police complaint, police told PTI news agency.
The girl, who was assaulted on Saturday morning, is in a stable condition. Doctors have confirmed she was raped.
Her family lives on the grounds of the embassy, where her father works as a member of the housekeeping staff.
Police said the accused, a driver, is not employed by the embassy. However, he lives with his parents in the embassy's staff quarters as his father works there.
The US embassy is located in Chanakyapuri, a smart diplomatic enclave in central Delhi which is home to several embassies and high commissions.
The heavily-guarded compound is spread over 28 acres and employs local staff.
The families of the accused and the victim knew each other well, according to investigators, who told the Hindustan Times newspaper that he "lured" the girl to his house when he saw her playing outside. His parents were away at the time of the attack.
When the girl returned home, she told her mother what had happened. She was immediately taken to hospital, where, police said, doctors confirmed that she had been raped.
Police said the man is being investigated under India's stringent child protection laws.
In 2018, the government introduced the death penalty for those who rape children amid an uproar over two high-profile cases - the rape and murder of an eight-year-old, and the rape of a 16-year-old.
According to India's latest crime figures, every fourth rape victim is a child. In an overwhelming number of rape cases - 94% - the victims know the perpetrators.
India's poor record of dealing with sexual violence came to the fore after the 2012 gang rape and murder of a student on a Delhi bus. This led to huge protests and changes to the country's rape laws.
In November, the gang rape and murder of a 27-year-old vet in the southern city of Hyderabad also made global headlines and sparked protests.