The Polish keeper needed lengthy treatment after a clash of heads with United's Phil Jones in the first half of Arsenal's 1-0 Premier League defeat at Old Trafford.
The 23-year-old did not immediately move after hitting the ground following the aerial collision but Arsenal's medical staff deemed him fit to continue.
The incident occurred just a week after Tottenham boss Andre Villas-Boas was heavily criticised for allowing keeper Hugo Lloris to play on after he was knocked out at Everton.
Wenger revealed that he did not talk to the team doctor after the incident, but insists that had he advised him to take Szczesny off he would have had no hesitation.
Wenger said: "Nobody told me anything about him. If he said there was a problem I would have taken him off. 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."