A shallow depression developed in the monsoon trough over the southeastern parts of the Solomon Islands late on 1 May. It moved slowly southwards and remained weak and ill-defined until 4 May when it started reintensifying gradually as it curved towards the southwest. Cloud convection and organisation increased and the system was named at 1800 UTC 4 May.
By 0000 UTC 5 May Meena was at 13.4°S, 160°E with a central pressure of 994 hPa. It moved southwest at around 20 km/h for 18 hours with little change in intensity to a position 15.0°S, 158.0°E then moved westerly for 12 hours, north-westerly for 12 hours and then west-northwesterly for 18 hours to 12.8°S, 149.7°E at 1200 UTC 7 May. The lowest central pressure during this period was 990 hPa at about 0600 UTC 6 May.
The final part of the track to landfall, on Cape York Peninsula, was almost due west. The system continually weakened and was barely a tropical cyclone at landfall at 0000 UTC 9 May when it had a central pressure of 1000 hPa. The system continued to weaken as it crossed Cape York Peninsula and dissipated in the central Gulf of Carpentaria 21 hours later.
The lowest observed pressure (1000 hPa) and strongest wind (93 km/h) were reported at 0600 on 6 May from a ship at 14.3°S and 154.7°E. No damage was reported.