The body of the 34-year-old woman had been found in an advanced state of decomposition last week in Paharganj, a favourite haunt of budget travellers near the capital's main train station.
Police official Devesh Chandra Srivastava told AFP the suspect had booked the guesthouse room in which the victim's body had been discovered.
He was the owner of a handicrafts shop in the area and had apparently fled before being arrested by police Sunday in Srinagar, the summer capital of Indian Kashmir, Srivastava said.
"We have yet to interrogate him properly," he added.
The victim has not been formally identified, but the Times of India quoted her sister as saying she was a schoolteacher who had arrived in India on March 19th.
The cause of death has also to be confirmed, although several media reports suggest she was strangled.
New Delhi is widely perceived as an unsafe city for women with official data showing that among the 35 biggest cities in the country, it has the largest numbers of crime cases against women.