The 28-year-old centre-back spent a spell on the sidelines with a similar problem last season.
He also missed the start of the season after surgery on a back injury before returning at the end of October.
"It is not a recurrence of the injury which required surgery so that is a positive," said Stoke boss Mark Hughes.
"Unfortunately, the negative is that he has soft muscle damage and at the moment it is looking like it will probably be three to four weeks I would think."
Shawcross will now miss the second leg of the Capital One Cup semi-final at Liverpool on Tuesday. The Reds beat Stoke 1-0 in the first leg.
The Potters also face an FA Cup fourth-round tie at Crystal Palace as well as Premier League games against Manchester United, Everton and Bournemouth in the next month.
Stoke City captain Ryan Shawcross could be out for up to a month with the back injury that forced him off in Saturday's defeat at Leicester.