The Manchester City midfielder aggravated a long-standing hamstring problem taking a shot during victory at Aston Villa on 4 March.
That meant another disruption to a debut season at Eastlands which has brought just 11 appearances, but Rodwell aims to be fit for April's FA Cup semi-final and to play his part in the Premier League run-in.
He told the club website: "Obviously you don't want to tempt fate but I'm not looking at this a lengthy absence and I hope to be back in a couple of weeks.
"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.
"The fans are the club as far as I'm concerned and it means a lot to know I have their backing and that they are so supportive towards me.
"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.
"This is an injury that can strike at any time to anyone and I'm sure it something that I'll be rid of before too long, but it's an on-going process and something that can't be rushed."