Crawley has been ruled out after he fractured the little finger on his right hand while attempting to take a catch during the recent third Test victory over the West Indies.
The 26-year-old will switch his attention to being fit for England's tour of Pakistan in October.
With Crawley sidelined, Dan Lawrence is set to open alongside Ben Duckett.
Lawrence has been included in several England squads but has not played a Test since 2022.
The 27-year-old moved from Essex to Surrey over the winter and has made an impressive start to the County Championship season, averaging 53.09 at a strike rate of 74.68 with two centuries and three fifties.
England made a number of changes to their side ahead of the West Indies series, handing Test debuts to Gus Atkinson and Jamie Smith, and there is now a first call-up for Essex batsman Jordan Cox.
The 23-year-old has been involved in the England set-up previously after joining the white-ball tour of Pakistan in 2022 and will be looking to make his international bow against Sri Lanka.
Uncapped seamer Dillon Pennington, who was in the squad for the 3-0 series win over the West Indies, joins Crawley on the sidelines after sustaining a hamstring injury playing for Northern Superchargers in The Hundred.
Pennington is likely to be sidelined for the rest of the English summer.
Nottinghamshire seam bowler Olly Stone returns to the Test squad for the first time since 2021 and will be hoping to add to his three Test caps.
The first Test against Sri Lanka starts at Old Trafford on August 21, with the second match at Lord's and the third at The Oval.
England squad for the Test series against Sri Lanka:
Ben Stokes (capt), Gus Atkinson, Shoaib Bashir, Harry Brook, Jordan Cox, Ben Duckett, Dan Lawrence, Ollie Pope, Matthew Potts, Joe Root, Jamie Smith, Olly Stone, Chris Woakes, Mark Wood
