A division bench of the court's Madurai bench, comprising Justices M.Venugopal and Abdul Qudhose, issued the order.
The petitioner K K Ramesh said the dengue menace was now a big challenge for the government.
The government did not take proper steps despite the court issuing several directions, he alleged.
He prayed that the court order a compensation of Rs.five lakh to the next of kin of those who died due to dengue.