The Italian international was substituted after 23 minutes at the Stadio Via del Mare.
"Fabio Quagliarella has undergone a CT scan at the Vito Fazzi hospital in Lecce, accompanied by club doctor Luca Stefanini," read a club statement.
"The scan has identified a full fracture of his right cheekbone arch.
"The 28-year-old is set to return to Turin with the squad and will remain overnight at the Fornaca clinic where he will be visited by Doctor Libero Tubino and, probably, tomorrow [Monday] undergo surgery to reduce the fracture."
Juventus are currently second in the Serie A table behind AC Milan.