Funk, 61, was previously boss at Scarborough and signed a two-year contract extension with AFC Mansfield back in January 2017.
A club statement said: "We would like to thank Rudy for the last four years, in what has been an incredible rise for this football club which has achieved the heights of the Northern Premier League thanks to the efforts of Rudy and his team.
"The club would like to put on record our gratefulness for Rudy’s efforts, and wish him all the best in his future endeavours.
"A further statement on the future of the manager’s position will be released in due course."
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