Rafael was making just his 11th appearance of the season in all competitions on Thursday but lasted just one half of their UEFA Europa League clash before he had to be substituted.
The club did not specify when the 23-year-old Brazilian goalkeeper will be available to play again.
"Rafael was found to have ruptured the anterior cruciate ligament in his right knee," the Serie A club said in a statement on Friday.
"The goalkeeper must now undergo surgery and then we will determine the recovery time. At the moment that is not possible."
Rafael joined Napoli from Brazilian club Santos at the start of the season for a reported fee of €5 million.
The injury to Rafael leaves Napoli short-handed in goal with the Brazilian the only other gloveman to have played during Rafael Benitez's tenure apart from number one custodian Pepe Reina.
Benitez's other options in goal are 38-year-old Roberto Colombo, who has not played a senior match in three seasons, and 17-year-old Nikita Baranovsky.
