The 22-year-old has been dogged by similar problems since joining City from Everton last summer and has been limited to four starts, with seven further appearances as a substitute.
Rodwell hoped a gruelling fitness programme and lifestyle changes had addressed the problem and he impressed in City's 2-0 victory over Chelsea last month but was then forced off only 25 minutes into their clash with Aston Villa two and a half weeks ago.
The midfielder told the club's official website: "It's just over two weeks into my injury now and it's healing well. I'm hoping for maybe another two weeks until I'm back on the pitch.
"I'll hopefully train within the next 10 days, that's my aim. If I do that, then it's been a really good rehab - four weeks is very good.
"If it takes a week more, then it will be a week more, just to be on the safe side, but we'll see - hopefully two more weeks is all I will need."
The recurrence of the injury was certainly a setback but Rodwell, who has been capped twice by England, is determined to think about the long term.
He said: "Initially it was depressing but I've got good people around me, good family, great physios, the sports science department are great and all the lads are brilliant, too.
"It's just a minor setback and it's a long career. I'm still young and I just have to stay positive."
- Sports & Recreation