Amit Singh, who is the son of a retired Assistant Commissioner of Police, was arrested from his house in Freedom Fighter's Colony in Neb Sarai.
He will be produced in a local court on Monday.
Singh is a physical training instructor at a private school in Gurgaon.
On May 26, an unidentified man tried to abduct the young Afghan woman when she, along with her husband, was going to buy medicine from a nearby market in South Delhi's Lajpat Nagar area.
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As locals and bystanders had rushed toward the car hearing the commotion, the man fled the scene in his car.
A complaint in this regard was registered by the husband of the victim.
The couple had told police that although they failed to note down the complete registration number of the Wagon-R car, but provided the last numbers of the car as "1160".
Investigators had set out to find the car, which was like finding a needle in a haystack.
"During questioning he confessed to the crime," said a senior police official.