The Spaniard picked up the injury in Stoke's 4-1 FA Cup defeat to Blackburn Rovers as he chased down Rovers' hat-trick hero Josh King on his way to a second of three goals.
Geoff Cameron was sent off in that game meaning he will be suspended for Saturday's trip to Aston Villa, while Erik Pieters (groin) and Ryan Shawcross (back) are injured and German defender Robert Huth is out on loan at Leicester City.
Marc Wilson may recover from a knock to feature at Villa Park, but manager Mark Hughes could be forced to put square pegs in round holes if not.
"We feared it was a really bad one," Hughes' assistant Mark Bowen told BBC Radio Stoke of Muniesa's ailment.
"He had a scan and they've come back saying it's four to six weeks.
"Ryan's had this back problem that he's had in the past and it's reared its ugly head again.
"He's gone in yesterday to see a specialist for some more injections.
"We're hoping it hit the right spot and, if so, over the next 48 hours it should progress significantly, but certainly not to put him in the frame for Saturday."
