Bowler Bresnan underwent surgery last month to correct a problem with his elbow and was expected to be fully fit for the upcoming Test series with Pakistan.
However, the decision to withdraw him from the touring party was made after a practice session earlier today.
"Bresnan tried to bowl today, having had an injection and a good rest," Strauss told reporters. "I think we were all expecting him to be absolutely fine. But it's very painful - and given that, he's probably not going to be able to play for two or three weeks.
"We're all gutted for him, because it's come from left-field. It's surprised him and us."
Graham Onions has taken Bresnan's place in the squad.