Ter Stegen's move from Borussia Monchengladbach was confirmed earlier this week, and Zubizarreta believes that the 22-year-old must immediately set a target of improving in his first season.
"Ter Stegen has a very difficult task, but it is an exciting one," Zubizarreta told reporters.
"It is one of the great challenges but we think he is capable of dealing with that and doing well.
"He is very fast, agile and very decisive. He's also very good in the air and one-on-ones. There is still room for improvement but we've all got time to improve."