The League Two club announced on Monday that they were looking to challenge the Football Association's decision to suspend the 23-year-old following an incident against Chesterfield on February 15.
However, Labadie has now accepted a charge of misconduct and will serve out his punishment.
"Torquay United can confirm that Joss Labadie has decided to withdraw his appeal and accept the FA charge for misconduct," read an official club statement. "Joss will now serve his 10-match ban with immediate effect."
In accepting the suspension, Labadie will now miss the rest of the season.