Shawcross was forced to sit out last weekend's win over Watford with the problem and Hughes has admitted unless he makes a remarkable recovery, the game against the Clarets will also come too soon.
Stoke are targeting back-to-back wins, but it looks like they will have to do it without Shawcross.
"Ryan is going out with the physios, he's not back with the group yet and so I think he has to be doubtful for the weekend again," the manager told reporters.
"It's a niggling injury right in the middle of the calf and you have to be careful with those because they can be a little big problematic if you come back too soon.
"We will be careful with him, he’s out with the physios, he could be back training with us tomorrow but if not then we'll take our time and see if we can get him back next week."
There is better news as both Glenn Whelan and Joe Allen are available again.