Germany international Ter Stegen underwent a successful operation on Monday after suffering a complete rupture of the patella tendon in his right knee.
The 32-year-old was injured in Barca's 5-1 LaLiga win at Villarreal on Sunday and is expected to be out for at least eight months, Spanish media reported.
"Inaki is doing very well, in pre-season too. He has worked very hard to be here. He is focused and ready to play," Flick told reporters ahead of Wednesday's home game with Getafe.
"We are confident but we also have to look at what we do because the players at the back are very young. For the moment, we don't feel under pressure and we trust in Inaki."
Having joined Barcelona's La Masia academy aged 13, the 25-year-old Pena has made 23 first-team appearances, conceding 39 goals and keeping five clean sheets.
"We will see what happens. We will talk to (Spain manager) Luis de la Fuente, who has coached world-class goalkeepers for many years. He will be the first person I will talk to," Flick added.
The Catalans were already without new signing Dani Olmo and fellow midfielders Gavi, Frenkie de Jong, Marc Bernal and Fermin Lopez plus defenders Ronald Araujo and Andreas Christensen.
Barca have made a perfect start to the season in LaLiga under Flick, with six straight wins putting them top of the table, four points ahead of champions Real Madrid in second, but the former Bayern Munich boss is striving for more.
"We analysed the game against Villarreal and we saw a lot of things that can be improved. We haven't reached the end of the road. You can always do more. We are moving forward step by step," Flick added.
