Appointed in April as the successor to James Colliver, the former Matlock Town boss stood down after his side's 3-0 defeat at Leek Town on Tuesday night left the world's oldest club third from bottom in EVO-STIK League South.
Hume, who also helped guide Bradford Park Avenue into the National League in 2010 during four and a half years as assistant manager, told fans in a short statement announcing his exit.
Hume, pictured, said: "For a number of reasons, things just haven't worked as I'd expected and for the benefit of this club, which I have a real feeling for, it is time for a change of manager. Everyone at the club has been really helpful and welcoming and I shall miss it."
A Sheffield FC spokesman said: "All of us at Sheffield FC would like to thank Mark for the effort and commitment made during his spell in charge and we wish him all the very best in the future."
Mark Shaw has been appointed as caretaker manager and will be assisted by Chris Dolby and Matt Roney. The trio will take charge for the first time on Saturday in league action at Romulus.
Image courtesy of Twitter
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