Shawcross had to come off in the first half of last Saturday's 3-1 Barclays Premier League win over QPR at the Britannia Stadium because of the problem.
And the Potters announced the news on their website on Friday that the 27-year-old centre-back now faces some time on the sidelines.
Manager Mark Hughes told Stoke City Player: "Unfortunately Ryan will be missing now for a couple of weeks.
"That is a big disappointment for us because he is obviously an important player for us and the captain, so he will be a miss.
"We do have other players who are capable of filling in though, so it is a chance for them to come in and make a mark - just as they have done in the past."
Jon Walters, who scored a hat-trick in the QPR game, is a doubt ahead of Sunday's league trip to Newcastle due to a knee problem which has prevented him training this week, although Hughes is hopeful the forward will be available.
Source : PA
Source: PA