The police said 22-year-old Akshay Gupta was arrested on a complaint filed by the woman.
She alleged that the incident took place when she, along with her cousin, had gone to Pulbangash Metro Station in Central Delhi.
The woman alleged that when they were entering the metro station, the man touched her inappropriately and started abusing her.
He also threatened to kill her if she declined his friendship proposal.
She said the accused had been stalking her for sometime.
Deputy Commissioner of Police (Metro) Pankaj Kumar Singh said a case was lodged at Rithala Metro Police Station and the man was arrested.