One coach of the Tamil Nadu Express from Delhi to Chennai caught fire as it was passing through Nellore station early on Monday.
The cause of the blaze is still unclear, but authorities suspect an electrical short circuit.
Accidents are common on India’s immense state-owned rail network.
In May, 24 people were killed when a passenger train crashed into a goods train, also in Andhra Pradesh state.
Most of the passengers were asleep when the fire broke out at 04:20 local time (22:50 GMT), said B Sridhar, head of Nellore’s district administration.
Some of them managed to jump off the moving train before it came to a halt, but 28 passengers in the coach were injured and taken to local hospitals.
The town of Nellore is about 500km (310 miles) south of Hyderabad, Andhra Pradesh’s district capital.
“I woke up after hearing loud screams. All I could see is black smoke,” Y Sampath, a software engineer who managed to escape the blaze, told The Hindu newspaper.
He was travelling with his sister, who is missing, the newspaper said.
The affected coach was completely gutted and rescue teams had to break in using special equipment.
Train accidents in India have killed 1,220 people over the past five years, railway officials recently revealed.
India’s railway operates 9,000 passenger trains and carries some 18 million passengers every day, connecting every corner of the country.