Senior Superintendent of Police Manu Maharaj told PTI that the person, suspected to the woman's love interest, had been evading the police dragnet since the incident on January 25.
He was arrested following a tip-off when he was planning to flee, the SSP said.
The Indore woman was shot dead allegedly by the man while she was going to Patna railway station in the auto rickshaw.
The woman had come to meet him and the man, who was accompanied by his cousin, allegedly pumped four bullets into her body.
Deputy Inspector General of Police Shalin said the police would take the killer in its custody after production in the court and interrogate him.