Jones, who netted his third goal in four games during the win at Coventry City at the weekend, was forced off in the second period at the Ricoh Arena with a dead leg.
Alex Gilliead, who Jones replaced as a first half substitute against Coventry, is to be sent for a scan on his injured hamstring, with McCall conceding the winger has no chance of making the trip to The Valley.
McCall says that Nicky Law will also be sidelined for the Charlton game due to the same knee problem that has ruled him out of City's last two matches.
Speaking ahead of the Addicks fixture, McCall said: "Jonesey (Alex Jones) has come in today (Monday) a lot better but I would still say he is 50-50 at the moment for Tuesday night.
"We will see what the physios think and assess him to see if he has any chance of travelling.
"We are aware that an injury like his can improve a lot in 24 hours.
"If he is available, we will definitely be taking him with us for the game.
"Nicky Law will train with the physios at the start of this week. Hopefully he can be back training with the rest of the squad Thursday or Friday.
"Gilly (Alex Gilliead) will go for a scan. We believe he may have a small tear in his hamstring.
"As we thought on Saturday, it looks like it could be between ten days and three weeks (out) for him. We will know more once we see the results of the scan though."