The former Rotherham United and Hartlepool United midfielder had been the successor to Craig Parry, having been appointed in April 2020.
He took charge of just seven Pitching In Northern Premier League N/West games, winning one against Pickering Town.
Pontefract’s statement said: “The directors and Andy Monkhouse have decided to part ways by mutual consent.
“We would like to thank Andy and his management team for all hard work during this difficult time for the whole country.
“We wish Andy all the best for the future.
“This is a very difficult time for all football clubs, but we look forward to better days in the future when we can all get back to supporting the club. In the meantime we hope everyone stays safe and well, we can’t wait to see you all back enjoying football at the Colls.”