The Gunners suffered a 2-1 defeat at the Emirates Stadium and will now be without Cech against second-placed Spurs on Saturday after he picked up the problem running back towards his own goal after going up for a stoppage-time corner.
David Ospina will come in to replace him for the first time in the Premier League this season.
Defender Laurent Koscielny, who missed the Swansea match with a calf injury, will also be absent for the crucial derby against Spurs.
Boss Arsene Wenger confirmed: "Cech got a muscular problem at the end of the game and he will not play on Saturday. I have full faith in Ospina.
"Cech struggled. He had a little groin problem before the game and I think he struggled a little bit.
"I don't know [how long he is out for], we have to see. It's a muscular problem, a calf problem and I don't know how long he will be out for.
"Koscielny has a calf problem as well. He will not play on Saturday."
