The full-back is expected to be out of action for at least two months after twisting his ankle during Saturday's 2-2 draw with Manchester City.
Despite Debuchy's absence from the side, Szczesny is hopeful that the France international will be back in training sooner rather than later.
"It's very disappointing to lose such an important player," he told the club's official website. "He's had a very strong start to the season, he's very experienced and he's a very solid right-back so we're disappointed to lose him but hopefully he'll be back as soon as possible."
Arsenal are back in action tonight when they get their Champions League campaign underway with a trip to Borussia Dortmund.