The League One club claimed they were only made aware by Her Majesty's Revenue & Customs on Friday that they had been called to defend the petition over monies due on 19 December last year.
They are adamant that all VAT and PAYE monies were up to date and branded the decision to bring the case to court a "disruptive and damaging" action.
The case was thrown out at a High Court hearing on Monday morning, and County are now expected to seek damages to recover legal costs and repair "the harm suffered by the Football Club".
A club statement read: "Notts County can confirm that the winding up petition brought against the club by Her Majesty's Revenue & Customs has been dismissed.
"The petition was dismissed in a matter of seconds at a hearing in London on Monday morning."
A statement released prior to the hearing read: "On Friday evening it was brought to the attention of the Notts County Chairman, Ray Trew, that the Football Club is due to appear in the High Court on Monday 11 February to defend a winding up petition.
"This action came without any prior notification to the Chairman and his fellow Directors. After investigation, it was found that this petition was being brought by Her Majesty's Revenue & Customs (HMRC) for PAYE payable on Wednesday 19 December 2012.
"The club can state, unequivocally, that the business is completely up to date with all VAT and PAYE monies and that this action is regarded by the Board as both disruptive and damaging.
"The board will be seeking legal advice regarding taking action against HMRC and the officer personally responsible for this and will seek to recover all costs associated with defending the action plus punitive damages for the harm suffered by the Football Club."