The Partenopei have made a terrific start to their league campaign, lying in second place behind Roma, while they also recorded a memorable victory over Borussia Dortmund in their opening Champions League game.
“With the fans passion they are conveying a positive energy,” Benitez told the club's official website.
“Their affection is really valued in a challenging season. The journey’s going to be long, but we have a competitive squad that is working to its maximum.
“We are working well and the team is growing. All the players are concentrating on taking this project towards its intended aims – not only for this year, but for next as well.”
The 53-year-old took charge of Napoli this summer, having been Chelsea's interim first-team manager last season.