The Englishman’s withdrawal means Rose – who finished tied-sixth when it was last held at St Andrews in 2015 and was joint runner-up to Molinari at Carnoustie in 2018 – will not be part of the field at The Open for the first time since 2006.
Hoshino was the first alternate after Alex Noren, the highest-ranked player not in the field, who made the decision to stay in the USA and compete in the Barracuda Championship rather than travel to Scotland.
England’s Aaron Rai, who posted a top-20 finish at Royal St George’s last year, also received a late call-up when South Africa’s Erik van Rooyen withdrew due to a neck injury ahead of his 1.48pm start.
The Japanese player missed the cut in last year’s contest, his only other appearance at The Open, with Hoshino primarily playing on the Japan Golf Tour.
Rose complained of pain during a practice round with Ryder Cup captain Henrik Stenson on the eve of the competition, and he was clearly in pain when warming up on the range on Thursday morning.
In a statement on Twitter, Rose said: “On the fourth hole yesterday, I made a swing with my driver and started to feel pain in my lower back. I’ve been getting around the clock treatment but it just doesn’t feel ready to compete in this prestigious championship.”