Wilshere has faced criticism at times over some indifferent performances, but the 22-year-old has shown glimpses of hitting top form - most notably a superb performance in the 2-2 Premier League draw with Manchester City last month.
Arsenal goalkeeper Szczesny is particularly impressed with the versatility Wilshere brings to the team and believes the only thing missing from the England international's game is regular goals.
"He has done well," Szczesny told Arsenal's official website. "Obviously there is a lot of competition for his spot because you have Mesut Ozil and Aaron Ramsey, plus Mikel [Arteta] and Mathieu [Flamini] playing that bit deeper.
"So it's hard for him but every time he has come in and got his chance he has done very well. He got a good goal against Man City - I'm not sure he meant that - but I'm very happy with him.
"He can go past players in midfield, which is a very important quality. We are all about passing the ball and moving it quickly, but sometimes if you can get past players in midfield it gives us a massive advantage - and Jack is very comfortable doing that.
"That is one of his biggest qualities. If he can just add a few more goals to his game then he will be pretty much a complete player for us."
Wilshere is often deployed in a more advanced role for Arsenal, while England manager Roy Hodgson has utilised him in a defensive midfield position.
And Szczesny believes it is a sign of Wilshere's quality that he is comfortable doing either job.
"You don't get too many midfielders who are [just] central midfielders - they are either defensive or attacking midfielders," he added. "Jack has a very good balance between the two.
"I don't think it is an argument whether he should be a defensive midfielder or a number 10. I am happy with him being very balanced between defending and attacking."
