Police said the man, a resident of Saravanampatti in the city, was taken into custody after tracing the 21-year-old woman's last call on her mobile.
Police started investigations after the woman's partents complained that she was missing since October 16.
During interrogation, the man confessed to killing and burying the body of the woman, with whom he was in love, police said.
Quoting the man, police said both had gone on a trip to Kallar on the border of Coimbatore and Nilgiris districts.
More From This Section
Fearing arrest if he left the body, he allegedly crushed her face by throwing a boulder and buried it there.
A special police team took the man to the place of occurrence this noon and exhumed the body, which was brought to the Coimbatore Medical College Hospital for post-mortem.
Further investigations are on.