The former Scotland captain joined Franco Smith's men in summer after departing Perpignan but he's been recovering from injury at Scotstoun.
Ritchie sustained an ankle issue at the French club and a pre-existing Achilles problem has subsequently flared up.
Glasgow start their United Rugby Championship campaign against Munster on Saturday but Ritchie won't feature.
The Warriors play six games before the international break and the fixtures in late-October against Benetton and the Lions are viewed as his most realistic targets for his maiden Glasgow bout.
Glasgow assistant coach Nigel Carolan told Scotland Rugby News: "Obviously, he came to us on the back of an issue with syndesmosis on his ankle. He also had little complications around his Achilles. So, look, they've all been mended. And I think he's working his way back. It will probably be the next few weeks.
"Hopefully, he'll be back before the November break. He's on target for then but he might be a little bit sooner. It's just a slower process because there were two little complications there, with both his ankle and also his Achilles.
"But he's tracking well. It's difficult when you join a club as well and he just wants to contribute on the field. And at the moment, it's just in meetings and he's sitting back and trying to learn how we do things. So it's tough for him because he just wants to get going."
Ritchie isn't the only Scotland international currently sidelined with Zander Fagerson, Kyle Steyn and Alex Samuel recovering from knocks sustained over the summer.
The vast majority of Glasgow's Scotland contingent didn't feature in pre-season and they'll be gradually reintroduced over the next three games ahead of the Champions Cup opener against Sale.
"It's very much around management and it's on an individual basis," said Carolan.
"Obviously, Franco and Gregor Townsend are in close alignment of who they want to see playing over the next few weeks. There's a number of guys there that have a high number of minutes, even on the back of last year.
"They'll try and put maybe a special priority on some guys over others. Guys like Zander Ferguson and Sione Tuipulotu. They've played a lot of rugby. Right through to the Six Nations, they've played a lot of games for us and were involved for most of the Nations [Championship] as well during the summer. So, everyone's going to be managed over the next few weeks.
“We hope again to see a few guys take the field this week. And then over the next couple of weeks, we'll try and drip-feed everybody else in."
Another player sidelined is Charlie Savala. The 26-year-old missed the entirety of the last campaign after joining from Northampton with a serious knee injury and he missed both Glasgow's pre-season friendlies with a knock.
"With Charlie, it's just about managing the load," said Carolan.
"It wasn't on his knee that had surgery. So, again, he ramped up his rehab over the summer there. It just had a negative effect on his opposite knee. But, again, he's close to returning. We'll hopefully see him in the next couple of weeks."
Alongside youngster Matthew Urwin, Savala will be expected to provide competition to Dan Lancaster at fly-half.
Lancaster enjoyed a promising maiden campaign at Scotstoun and Glasgow decided against signing an inexperienced number ten this summer, despite the departures of international calibre stars in Adam Hastings and Tom Jordan over the last two years.
On that decision, Carolan explained: "The evolution of our club is to bring in another 10, we'd have to be looking for a Scottish qualified [player]. We brought in Dan Lancaster, who's Scottish qualified. Charlie Savala is Scottish qualified.
"And Matty Urwin is Scottish qualified. So we weren't going to pay the type of money you pay for a foreign 10 to come in and take the place of these guys. We're very, very happy with where Dan Lancaster is at in terms of his development.
"If he can keep going the way he is. It's only natural that the guys in Scotland will start to take notice. Again, I think Matty Urwin has got a very bright future ahead of him as well.
"So we didn't really discuss bringing in a 10. We did bring in Bailey Kuenzle. We needed a utility player. And what we've seen from him so far is he's, we're calling him the Swiss army knife. We put him on the wing, put him at ten, put him at centre. He's a box of tricks and he's fitted in really well so far."