The Liverpool full-back, whose inclusion in Gareth Southgate's squad was one of the biggest talking points around the initial announcement, was forced off with an injury late on in England's friendly against Austria on Wednesday night.
Alexander-Arnold has now been ruled out for up to six weeks following a scan, meaning he will miss the Euros.
Addressing the issue publicly for the first time on Friday, the 22-year-old tweeted to say he was "absolutely gutted”.
England manager Southgate will name a replacement for the right-back after Sunday's second and final warm-up game against Romania in Middlesbrough.
Southampton captain James Ward-Prowse, Manchester United's Jesse Lingard and Brighton defender Ben White are all contenders to come into the squad.
England can make unlimited changes to their 26-man list due to new injuries before the opening game against Croatia on June 13.