Police said the woman from Salem district had come to Bhavani Taluk a few days ago to lend some money to her relative Muthuswamy.
When she did not return home, her husband complained to Kolathur police who transferred the case to Vellitirupur police.
Vellitirupur police after investigation took Muthuwamy and his fried Yuvaraj into custody for questioning.
Police said Muthuswamy admitted that when she came to his place, he and his friend took her to an isolated area and strangulated her to death and then buried the body in a nearby land.
A murder case has been registered against the two.