Pitchai, in-charge of Environment, Pollution Control and Minorities Welfare portfolios, died on the spot when his car collided with a lorry at Tiruvelankurichi, about 40 km from here, police said.
He was sworn-in on May 16 following the AIADMK-led front's landslide victory in the assembly polls.
The lorry had sped away, police said, adding only after apprehending the driver complete details of the accident can be known.
The 60-year-old minister was proceeding to Chennai after garlanding the statue of community leader Perumpidugu Mutharayar when the mishap occurred, which left five others including his driver injured, police said.
Speaking to reporters here after paying homage to the minister by placing a wreathe on his body, Jayalalithaa said "the public and her partymen suspect that there is some mystery about the accident. Police have registered a case and it will be transferred to the CB-CID," she said.
She said if anybody was found guilty they would be tried as per the law.
The minister's car driver told the police that the lorry with Kerala registration had "deliberately" swerved towards the minister's car and hit the spot where Pitchai was sitting, and he suspected that it was not an accident.
Jayalalithaa who arrived by a special flight from Chennai offered condolence to the minister's wife Fathima Beevi and other family members. All the shops in the city remained closed and most of the buses did not ply in the city.