The body of Rupa Parkar, from Sanvordem village, was found in bushes near the village on May 6 and the accused, Hussain Khan (40), who worked as a driver with a private firm, was arrested on Saturday, Superintendent of Police (South Goa) Abhishek Dhania told PTI.
While investigating the case, the police rounded up 50 suspects before zeroing in on Hussain, he said.
The accused told the police that he had offered lift to the woman while she was waiting for a bus. He later took her to an isolated spot and allegedly killed her by hitting on her head with an iron rod, the official said.
The man also told the police that he had killed the woman to rob her gold chain, which he later pawned to get a loan and purchased a two-wheeler, the official added.