Jones, who rejoined Glasgow in the summer from Harlequins, aggravated a back problem in Quins' Premiership semi-final loss to Saracens in June.
Jones missed Scotland's summer tour to South America but it was hoped that he would recover in time for the start of the URC season, but the injury isn't healing as quickly as had been hoped.
"I think he's six to seven weeks away, so he's a long way off," said Head Coach Franco Smith in The Scotsman.
"We're being very conservative around it. For now, it's in the medical team's hands. So, we just have to be patient. He hasn't put his boots on yet.
"He's a player we'll need in the second part [of the season]. There's no need for me to rush him. To rush him back for one or two games before the break in November is going to be mismanagement of the player.
"So, we'll give him the right amount of time so that he can come back with the intent to perform and not just the intent to play."