Concerns were raised about Szczesny when he required lengthy treatment after a clash of heads with United's Phil Jones in the first half of the 1-0 Premier League loss at Old Trafford.
Wenger said: "I listen to the doctor. If he says to me he has to come off, he comes off.
"No matter if we have seven men on the field, I do it.
"You have only one life and you have 60 games per year."
When asked if the doctor had told him Szczesny was fit, Wenger, speaking in his post-match press conference, said: "No, nobody told me anything about him.
"If he said there was a problem I would have taken him off."
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