The Catalans pair both left the field through injury in Sunday’s Magic Weekend draw against Huddersfield.
Carney suffered a torn pectoral muscle in a challenge on Kyle Wood towards the end of the game, which saw the Giants steal a point with a touchline conversion on the hooter.
It was only his seventh appearance for the French side since his arrival in the close season.
Meanwhile, Tonga will also be missing for most of the next two months with a broken jaw, and he will undergo surgery on Tuesday morning.
The centre was forced off injured after just 12 seconds of his debut against St Helens in February, though he has gone on to score six tries in 16 appearances for the Dragons since.