The couple from Puducherry were said to be upset over the sexual assault of their teenaged daughter two days ago by a youth, who was later arrested.
With their daughter, the couple, after visiting Palani temple, came to Tirupur on Saturday, police said.
The father of the girl purchased poison and mixed it with soft drinks and gave it to his wife and daughter.
The couple started vomiting after sometime and hearing the screams of their daughter, passersby called ambulance and took them to the government hospital. The couple died in the night.
Police have handed over the daughter to a shelter home in Tirupur.