The 22-year-old Polish international was dropped last month in favour of the returning Lukas Fabianski, who has conceded just one goal in three appearances for the Gunners.
Szczesny was omitted from the Arsenal side that won 2-0 against Bayern Munich at the Allianz Arena in the Champions League last month, with Wenger citing 'mental fatigue' as the reason the stopper did not fly to Germany.
Now, Seaman has called for the youngster to prove his strength of character, and fight for his right to return to the starting line-up.
"All goalkeepers make mistakes but the really good ones learn from them and show they are able to bounce back from a setback," he explained. "You have to recognise where you have gone wrong, admit you made an error and work hard to put it right.
"It's important to have a lot of self-confidence as a goalkeeper and you need to be strong enough to tell your defence when they have gone wrong. But you never stop learning and the best goalkeepers recognise that."
With 406 senior Arsenal appearances to his name as well as 75 England caps, Seaman is well-placed to offer advice to Szczesny, who still has the potential to develop into a world-class goalkeeper in the future.
And, while the Pole's lack of action must be frustrating for the player personally, from a club perspective the increased competition for places at the Emirates Stadium can only be a good thing.
"I don't know if Szczesny will win back his number one spot. It's quite interesting with Fabianski doing really well," Seaman added. "He's worked really hard since his injury and he looks a totally different goalkeeper.
"But it's great to have that competition. It's important to show you have the right character to be back on track.
"Look at David de Gea at Manchester United, that's exactly what he has done. He had a wobble but was mentally strong and bounced back and now everyone is rightly praising him for being a great goalkeeper."