Kompany limped off just past the half-hour mark at the Britannia Stadium and, according to assistant boss David Platt, faces a race against time to be fit to take on Liverpool next Sunday.
"I think we'll lose Vincent for a little while," said Platt on City's official website after the 1-0 victory in the fourth round clash.
"It's too early to say how long he will be out but he has a slight pull on his calf and will miss the midweek game.
"We will have to assess the injury over the next 24 hours to get a better picture but he won't play against QPR."
On the performance in the Potteries, which saw Pablo Zabaleta grab the only goal in the closing stages, Platt added: "We had a number of chances so we're disappointed we've not won by more but everyone knows this is a tough place to come at the best of times so we have to be happy.
"I thought our defenders were excellent today and did exactly what you need to do when facing the aerial threat Stoke pose so on that score, we're very happy to leave here with a clean sheet.
"It wasn't strange to see Pablo in that area because he often supports the attack and we encourage our full-backs to get forward whenever they can.
"He was in the right place and took the opportunity really well. We want to win both competitions that we're still involved in and we'll look forward to the draw on Sunday."