The model contains a chip that "pairs" a screen with a specific phone and requires special software tools to "match" a new one.
Repair firms have found that without those tools, the facial-identification security function no longer works.
Apple, whose repairers use the tools, says it will issue a software update.
The feature has been widely criticised by right-to-repair advocates, who suggest it was included to limit who could repair iPhones.
The issue was first reported by iFixit, a company specialising in tools, parts and tech repair guides.
It labelled the new link between screen replacements and Face ID as a "dark day for fixers, both DIY and professional".