The powerful opening batter was named in a provisional group of 15 players for the tournament in India but the combination of his own injury problems, Dawid Malan's outstanding form and the growing claims of Harry Brook have cost him his place.
Back spasms ruled Roy out of the recent series against New Zealand, which England won 3-1, meaning he was unable to make a case for himself.
Roy averages nearly 40 in 116 50-over one-day internationals.
‘Not a decision taken lightly’
"It's not a decision we've taken lightly," said Wright. "In the early squad, we had him down for opening the batting with Jonny Bairstow in the World Cup... but things happen in sport, injuries happen.
"Everyone was told 'Look, this is the 15 we're looking to take to the World Cup', but unfortunately that's the ruthless side of sport isn't it? It's not the nice side of sport that changes do have to be made.”
Wright said Roy had turned down the chance to play in the ODI series against Ireland starting this week, but that he remained an option as a World Cup replacement if required.
It is not clear whether the 33-year-old, who was part of England's victorious team on home soil four years ago, will make himself available for the defending champions.
"As you can imagine, he's absolutely gutted and I wouldn't expect anything else. I feel for him, as I feel for anyone you leave out," said Wright.
"We certainly haven't ruled him out. For Jason now, I'm sure he's got some thinking to do over the initial disappointment, but we've made clear that if there's an injury at the top of the order, there's definitely the option for him to come in as the reserve.”
England play New Zealand in the opening match of the World Cup on October 5.