The Hatters, who were relegated from the Football League last season, are 17th in the Conference after 19 games of 2011-12.
Hamann's time at Edgeley Park has coincided with a period of boardroom uncertainty.
He wrote on the club's website: "Following a meeting this morning between Lord Snape and myself I have tendered my resignation as manager of Stockport County.
"Having been introduced to the club by Tony Evans, I presumed that the takeover by him and his consortium would have taken place. Various promises were made to me at the time of my appointment which subsequently did not take place. I feel therefore unable to continue in post.
"I wish to thank the club and its supporters for their encouragement and commitment over the past few months and wish Stockport County well for the future."