Curran, 28, was suggested as a possible replacement for former England Test captain Ben Stokes following his fellow all-rounder's shock international retirement at the conclusion of a series loss to New Zealand in June.
But he suffered a groin injury playing for MI London in the domestic Hundred competition. Curran will now undergo surgery on Friday and will not feature again this season.
Curran made his Test debut as a 19-year old in 2018 and has made 24 appearances in the format, the last in 2021, although he is now a regular in England's white-ball set-up.
But after Stokes's exit, England selector Marcus North said Curran came under serious consideration for the current home series against Pakistan.
Curran is also joined on the injury list by fellow potential Stokes replacement Will Jacks, who is currently recovering from an appendix operation.