"As the wind speed is around 50 knots, it is not conducive to operate the flights. We have not closed the airport," Chennai Airport Director Deepak Shastri told IANS.
Around 500 passengers - out and inbound - will be in the domestic terminal.
He said: "Twenty flights have been diverted, nine got delayed and five were cancelled."
According to him, since last night and till the flight operations were stopped, 46 flights were operated from the airport.
He said the incoming flights were diverted to nearby cities like Bengaluru or Coimbatore.
Shastri said the strong wind situation would persist till 3 p.m.
"The runway is open and is not flooded," Shastri added.