The Tudors are currently on a rotten run and have suffered nine straight defeats in all competitions - conceding 12 goals in their last two games.
Wilkinson's last win came two months ago in September when they defeated Slough Town 1-0, part of a nine-game unbeaten start to the National League South season.
But a plethora of injuries has seen the club fall down the table and they now sit 17th in the table.
A club statement read: "The club would like to put on record our thanks for the hard work that Bobby has put into the club over his time here, the strong start to the season created some great memories for our fans.
"The club acknowledges the impact that injuries have had on the squad and the challenges that this created.
"We wish Bobby and his management team all the best in their future careers.
"Following his departure, Bobby would like to put on his record his thanks to everyone at the football club, the Chairman, Committee and most importantly the fans who have supported him through these very challenging last six weeks.
"The Club remain committed to finishing the season strongly and are actively working on confirming a new management team.
"Further details will be communicated in due course.
"We appreciate the understanding and continued support of our supporters during this transitional period."