Martins Indi suffered a groin strain while playing for his club during their 0-0 draw against Liverpool last weekend.
The Potters will also be without the services of Maxim Choupo-Moting, who is getting back to fitness, and Kostas Stafylidis, who has a rib injury.
Potters manager Paul Lambert said: "Bruno [Martins Indi] is struggling and he is out. We'll have to see if Bruno can make the Swansea game.
"Glen [Johnson] has trained and we will see how he is, but other than that it's the same group as Anfield.
"Max Choupo-Moting has started light training. Stafylidis's ribs are still a bit of a concern but doing better."