Wilson, 59, managed Barnsley and Sheffield Wednesday in the top flight in the 1990s, and had been helping the Bucks following the departure of manager Paul Phillips last week.
A club spokesperson said: "The club would like to thank former Premiership manager Danny Wilson for taking charge of the side for the visit of Mickleover Sports yesterday and for his work for the club in training last week.
"The search for a new manager should be resolved this week with news on our social media outlets when known."
Stuart Beavon scored the only goal of the game to complete a first ever double over Buxton for Mickleover.
Keep up-to-date with our exclusive email newsletters.
Subscribe