Mohd Shah Hussain was apprehended from his rented house in Gurgaon. He was found doing tyre puncture repair work there, Chhaya Sharma, Deputy Commissioner of Police (South), said.
A senior police official said he was declared a proclaimed offender in the case. Bihar Police have been told about his arrest.
Falak was admitted to hospital with severe bruises on her body, head injuries and broken arms on January 18. Her head was badly smashed, she had broken arms, bite marks all over her body and her cheeks branded with hot iron. She died on March 16.
Hussain was wanted in connection with the gang rape case of 2010 in Muzffarpur.
"Hussain, who has a notorious name Silothi in the crime field, had committed gang rape with his associate Tiya. Tiya surrenedered before the court but Hussain had been absconding and has been hiding in Gurgaon," Sharma said.
"He was not even turning up to take home his wife Munni Khatoon and two minor children aged 9 yrs and 6 yrs," she said.
The help of Mohd Munif, the brother-in-law of Hussain, was taken to ascertain his identity, she said.