Nimely collided with Aston Villa's goalkeeper after scoring the opening goal in last week's 2-0 win for City's Elite Development Squad at Hyde and was forced to limp off as a result.
"We're planning to be without Alex for a little while," said EDS boss Andy Welsh to City's website. "It's rotten luck on the lad, particularly as we are so early into the new season.
"He has been playing really well and it was unfortunate that he picked this up after scoring a goal, but these things happen in football.
"It's hard to estimate the exact period of time he'll be missing, but it will probably take between six to eight weeks to fully recover."