There is no direct connection from Madurai to Thekkady. However, you can take the night train to Rajapalayam (RJPM) then take the taxi to Thekkady. Alternatively, you can travel from Madurai to Thekkady in around 2 h 20 min.
From Madurai Junction (MDU) night train to Rajapalayam (RJPM) then taxi to Thekkady. 4 h 25 min ₹5,205. From Madurai taxi to Thekkady. 2 h 20 min ₹3,914. From Madurai drive to Thekkady. 2 h 20 min ₹1,133.