The former Everton player is expected to be ruled out for around a fortnight for aggravating a hamstring problem during City's 1-0 victory over Aston Villa last week.
"Obviously you don't want to tempt fate but I'm not looking at this as a lengthy absence and I hope to be back in a couple of weeks," Rodwell told the club's official website.
"One thing I would like to say is a big thank you to all our supporters. I've had loads of good will messages saying to keep my chin up and that's I'll be back before too long.
"Hopefully I can play my part in the run-in and help us win some silverware and end what has been a frustrating season on a high."
City, who sit 12 points adrift of league leaders Manchester United, have 10 games remaining, as well as an FA Cup semi-final against United or Chelsea.