Sanju, 24, teamed up with three friends and abducted on Sunday morning the girl's father (name withheld) from the shop where he worked in Dwarka area.
Sanju then forced the captive father to telephone his daughter and tell her that she should marry Sanju as he was "a good boy".
The father also blurted out that he was in Sonepat in Haryana.
By then, the police had been called in.
"Sanju was arrested on Monday night from Mathura with the help of technical surveillance after a team headed by ACP Rajinder Singh Yadav and Inspector Sanjay Kumar rescued the victim," Deputy Commissioner of Police Anto Alphonse said.
"The daughter told investigators that she knew Sanju and suspected he could have kidnapped her father. The police teams tracked the locations of the mobile numbers from where calls had been made to the girl in Baraut, Meerut and finally Mathura," the officer said.
During sustained interrogation, Sanju disclosed that he wanted to marry the man's daughter but he was opposed to their union and had also shifted his daughter to their native place.
"Sanju borrowed a car from a friend and joined three friends to execute his crime. A hunt is on to nab his friends," the officer added.
( With inputs from IANS )