The 10km (6.2-mile) stretch of elevated track has seven stations and connects Alandur to Koyambedu.
The journey takes 15 minutes - the metro is expected to ease traffic congestion.
The construction is part of a proposed 45km (27-mile) network which is due to be completed by 2015.
Chennai is the sixth Indian city to have the metro after Delhi, Kolkata, Bangalore, Mumbai and Jaipur.
The Chennai metro was inaugurated on Monday by Tamil Nadu Chief Minister J Jayalalitha.
The first train was driven by a 28-year-old woman, A Preethi, an engineering diploma holder, reports say.
"I am excited, my daughter's dream of becoming a loco pilot (driver) of Metro Rail has come true," Ms Preethi's father R Anbu told Press Trust of India news agency.
"She quit her first job, applied for a job in Chennai metro rail, and she was the first woman to get selected. Three other women joined as pilots after her and I am happy that she was successful," he said.
The 45km (27 miles)-long, 32-station service will eventually run on two corridors in the city:  Washermenpet to Chennai Airport and Chennai Central to St Thomas Mount.
A journalist tweeted about her first experience on the service:
A metro rail service has been launched in the southern Indian city of Chennai, making it the sixth Indian city to get the service.