Maciej Szczesny, who won seven caps for Poland, insisted Wenger was to blame for his son's poor form while also suggesting that he had been forced to play on through injuries.
But Szczesny jnr, currently competing with Artur Boruc for the goalkeeping role with Poland, responded by claiming he did not subscribe to his father's opinions.
In a statement on the Arsenal website, Szczesny said: "I would like to apologise for the comments made by my father which have been used by both Polish and English media.
"I'd like to make it clear that those were the views and opinions of my father and not mine, and although I respect his views I cannot accept them as I find them disrespectful to the club I truly love.
"I have been at Arsenal Football Club for seven years now and I have always shown my full respect to the club, Arsene Wenger, all the coaching staff, my team-mates and the fans.
"I've always felt that I received great support from the manager and the fans and I am fully focused on getting back to my best. I am proud to be a part of Arsenal and I see my future at this great club."
Szczesny was dropped for the UEFA Champions League clash with Bayern Munich last week, and he was left on the bench for the weekend win over Swansea with Wenger claiming he was "mentally affected" by playing too many games.
Wenger's decision prompted an angry outburst from Szczesny snr, who said his son had been made a "scapegoat" for Arsenal's indifferent form this season.