The former Premier League midfielder was let go on Sunday after Notts fell to their fourth League Two defeat in a row at Lincoln City.
On Sunday evening, Nottinghamshire resident Enever quit the board.
"After some serious soul searching I've decided to step down as a board director of Notts County Football Club," he wrote on Twitter.
"For the majority of the time it's been a huge privilege to be involved with the World's oldest league club.
"I've worked with, and met, some fantastic people who genuinely have the best interests of the football club at heart.
"As an individual I need to be true to my own values and be honest enough to know when my ability to influence matters is restricted.
"I wish the club every success for the future and hope the former management team will be successful in their careers."
A second board member may also have stepped down too, with Darren Fletcher removing the role of Notts board member from his Twitter profile.
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