The 27-year-old has been struggling with an elbow injury during England's ongoing one-day series with India, and Miller believes that Bresnan needs to resolve the problem before the summer.
Miller told reporters: "Tim had got a little issue with his elbow, which he has had for a while. He's had a problem and he felt that playing through it could alleviate that problem, but that hasn't been the case.
"He needs it looked at because it's not right at the moment. This was an opportunity for him to go back and get it sorted.
"He'll have a look with the specialists and see what's needed. It's not necessarily an operation at this stage and we feel he'll be absolutely fine; our medical staff say he'll be fine for the summer."
Bresnan has been replaced on the tour by Chris Woakes.