The 39-year-old's resignation comes just a month after he was appointed to the job, with a club statement blaming a "misunderstanding" related to comments made by president Maurizio Zamperini.
The Sicilian outfit have thanked the former Italy international for his work at the club despite his short stay.
"Our technical director Christian Panucci has resigned due to a misunderstanding of statements made by president Maurizio Zamparini, which were incorrectly reported by some newspapers," read the statement.
"The club accept Panucci's decision with deep regret and thank him for the work he did in a short period."
Panucci was capped 57 times for his country.