Arzani joined the Scottish giants on a two-year loan deal from Manchester City following the 2018 FIFA World Cup and arrived with high expectations after dazzling defences in Russia.
An anterior cruciate ligament injury on debut last November soon disrupted the 20-year-old's development and Schwarzer believes the move may have come too soon in his career.
"Daniel Arzani is one of those players who has been incredibly exciting, particularly leading up to the World Cup in 2018," Schwarzer told Goal.
"He had a phenomenal breakthrough season in the A-League.
"He didn't play enough games over 90 minutes, which is something he needs to build on.
"The Celtic move is one which I am not sure is the best move for him just yet. But it is about playing games and continuing to develop.
"His injury came at the very worst time as he just arrived and got his first opportunity to play from the start.
"It was not only unfortunate for his career at Celtic but also for Australia. I just hope that he can get back to the level he was at before his injury.
"He is a huge emerging talent from Australia. That's why Man City signed him. I know he was at their sister club in Melbourne.
"He is a huge talent. He is very unpredictable. We haven't had a player like that for a very long time."
Arzani has since returned to Celtic training and is nearing full fitness ahead of an anticipated first-team return at the end of the month.
