The Demons were dealt a double dose of "devastating" news on Monday when it was confirmed Melksham and Luke Dunstan had suffered ACL tears.
Melksham, who has kicked 16 goals since being recalled in round 16, ruptured his ACL while trying to change direction during the third quarter of Melbourne's 21-point win over Sydney on Sunday.
The timing of the blow is particularly cruel for Melksham, who missed out on the Demons' 2021 flag.
Melksham turns 32 on Tuesday, and it remains to be seen if he'll earn a new deal at Melbourne on the back of the long-term knee injury.
Dunstan, who hasn't featured for the Demons at senior level this season, suffered his ACL tear while playing in the VFL over the weekend.
Melbourne finished fourth on the ladder and will face minor premiers Collingwood in a qualifying final on Thursday, September 7 at the MCG.
"Unfortunately, scans confirmed the worst for Jake and Luke this afternoon," Melbourne's general manager of AFL Performance Alan Richardson said in a statement.
"It is incredibly disappointing news for both players, particularly on the eve of an AFL and VFL Finals Series. It really is a cruel part of our game.
"Jake and Luke have played very important roles for us in recent weeks and have done so with class and character.Â
"It is devastating to lose them at this point, but I have no doubt they will apply the same attitude and commitment to their respective rehabs.
"Both players mean a lot to our football club, and we will be doing everything we can to support them through this difficult time."