The accused, Chetan Prakash, was arrested from Karol Bagh in central Delhi.
The incident occurred April 17 at the victim's house in Swaroop Nagar in north Delhi.
On the fateful day, Prakash visited Rakhi, 28. She complained to Prakash that he had stopped giving her gifts after he married her sister, said a police officer yesterday.
"When Prakash told Rakhi that he would not be able to give her gifts, she threatened him that she would disclose their illicit relationship," the officer said.
"He strangled her with her dupatta while she was cleaning the kitchen," he added.
"The accused took away the victim's valuables to give the impression that a robbery was behind the murder," he said.