The midfielder was forced to limp out of City's 1-0 win at Villa Park with a hamstring strain.
Rodwell's debut season with City has been blighted by hamstring trouble, with Mancini admitting that his medical team are no closer to finding a long-term solution to the issue.
He told PA: "We are very sorry for Jack, because he is a good guy, a good player, but he is unlucky. It is his hamstring.
"I think it is impossible to resolve his problem after six or seven months because he's had this problem for five or six years and we need maybe more time. How long will he be out? Maybe he will be back after the international break, three or four weeks. It is the same injury.
"I am very sorry because he is a young player. He needs to improve but he has played very well against Chelsea and was playing very well tonight."
Mancini also confirmed that the 21-year-old will now spend at least three weeks on the injury list.