The influential 30-year-old defender has not featured for the Potters since the 1-1 draw with West Bromwich Albion at the Hawthorns on August 27 after suffering the back problem ahead of the 2-2 home draw with Manchester United on September 9.
Shawcross has been working hard on his bid to return to action, but assistant boss Bowen has confirmed that he will not be back for Saturday's trip to Manchester City and the club have no specific target with regards to a comeback date.
He said on the club's website: "He's been getting on with his recovery and having injections, but obviously he's not available for the weekend.
"I had a brief chat with him and he said it’s a case of not putting any deadlines on himself - the bottom line is he’s got to make sure he's right.
"It's important for him and for us to get him back on the field, but back on the field for a sustained challenge for the rest of the season, not to be in for a week or so and then back out again."