The 22-year-old man later surrendered to police.
The victim hailed from Darjeeling and had fallen in love with him and moved to the city about three months ago, police said.
While the deceased was working in a textile store, the man was working as an accountant at a sports store in the city, police said.
The couple, staying with their relatives, had engaged in an argument last night and the wife reportedly threatened to go back to Darjeeling, police said.
He immediately surrendered to Variety Hall Road police, just 100 metres from the office, even as a team of medical assistants, who rushed to the spot, found the woman dead, police said.