Roy was hit on the neck during training on Tuesday and although the 29-year-old passed required concussion protocols on Wednesday, the England and Wales Cricket Board (ECB) has decided to have an additional batsman as cover at the top of the order. Surrey confirmed 21-year-old Pope's inclusion in a tweet.
Pope has featured for England in only two Tests in his career, both against India last year, scoring 54 runs in three innings before picking up a shoulder injury that required surgery.
He scored an unbeaten 221 off 337 balls in the County Championship clash against Hampshire at The Oval on Wednesday before heading to Leeds.
Australia batsman Steve Smith was ruled out of the third Test due to the concussion he suffered at Lord's in the drawn second Test.
The visitors lead the series 1-0 having won the first Test by 251 runs.