The Pole has joined Brentford on a month's loan.
Poland international Szczesny, 19, joined the Gunners two years ago and made his debut in the Carling Cup win over West Brom in September.
Brentford boss Andy Scott said: "This is another good signing for the club.
"He brings with him more of the quality that we are looking to introduce into the squad.
"It also shows our capability to bring in good players. We are looking forward to working with him and enjoying a fruitful relationship."