In 2013, Gutiérrez joined the Formula 1 grid with Sauber but lost his seat at the end of 2014, having not earned any points for the Swiss team.
In mid-December Gutiérrez was announced as Ferrari's new test and reserve driver and Arrivabene believes he will be given another chance to prove himself in Formula 1.
"He is a driver that made his debut in F1 too soon," Arrivabene said of 23-year-old Gutiérrez.
"Talented drivers must not be thrown on to the scene too early. I am sure he is talented and will have a chance to show it."
The Mexican youngster is not Ferrari’s only test driver with the team also having Jean-Eric Vergne as a back-up to regular drivers Sebastian Vettel and Kimi Raikkonen.