The centre-back was brought off in the 42nd minute of Saturday's clash at the Britannia Stadium, having missed a trip to Leicester City earlier in January.
And he will now sit out Sunday's Premier League match at Newcastle United, as well as the subsequent home game against Manchester City and an FA Cup fifth round tie with Blackburn Rovers.
"Unfortunately Ryan will be missing now for a couple of weeks," Stoke manager Mark Hughes told the club's official website.
"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."
Marc Muniesa replaced Shawcross against QPR and partnered Philipp Wollscheid in the heart of Stoke's defence.
Hughes - who will again be without left-back Erik Pieters this weekend - is hopeful striker Jonathan Walters will be able to feature at Newcastle despite a knee complaint.
Walters scored his first Premier League hat-trick in Saturday's triumph over QPR, but has not trained since.
"Jon hasn't trained since the game because of a little problem with his knee, which we are trying to manage at the moment," Hughes added.
"Hopefully that will have settled in time for the game on Sunday – we are hopeful of having him available to us."
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