The accused Mathanraj, a fisherman by profession, surrendered before the police a few hours after the incident.
The victim was an engineering student from Chellanenthal village in Pudukottai district, police said and added that she was studying first year B.Tech in a college in Chennai.
According to police, the girl fell in love with Mathanraj, who stayed at Jagadapattinam in Pudukottai district for fishing.
After joining the engineering course, she had reportedly started avoiding him.
Mathanraj had subsequently gone through her Facebook profile and found that she had made some new friends, who were her college-mates. Also, he was under the impression that she was avoiding him due to her new friends.
She left Chennai to travel to her native place yesterday.
Early this morning, he met the girl at Mayiladuthurai bus stand and persuaded her to go with him to Poompuhar.
During a chat at the Poompuhar beach when the girl reportedly told Mathanraj that she was not interested in him, he got furious and attacked her with a big stone.
She fell down in a pool of blood and died on the spot following which Mathanraj fled the scene.
On finding the girl's body in a pool of blood, fishermen who happened to pass through that stretch informed Poompuhar police.
Sirkazhi DSP Sekar, Poompuhar police inspector Singaravel and other officials rushed to the spot and sent the body to Sirkazhi GH for postmortem.