The Brighton defender has been struggling with a niggling injury of late and has decided to pull out of the Three Lions' squad.
Commenting on his decision, Dunk said: "I was proud to be recalled to the England squad. My first England cap remains one of the proudest moments of my career.
"I never gave up hope, and I hope that opportunity will come again.
"I'm sorry it won't be this summer but at the end of the season, a few of us had to step up to achieve our aim of European football.
"A few of us were playing on adrenaline, pushing ourselves through games. I had a couple of injury issues, but our aim was to secure that top six place and create history.
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"I spoke to Gareth Southgate at the end of the season, after we'd achieved that. I explained that I thought I might not be fit in time for the games against Malta and North Macedonia.
"I didn't want to mess him around for two important qualifiers for the country.
"He was excellent with me, told me to take as long as possible and give myself the best chance to be part of the squad. I'd like to thank him for that support, and wish the squad well for the two games."
England are currently preparing to face Malta next Friday, before pitting their wits against North Macedonia on June 19.
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Dunk is the only player from Gareth Southgate's original 25-man squad not due to report to St George's Park this week.
Meanwhile Jude Bellingham will also play no part as he recovers from an ongoing knee injury.
His niggle kept him out of Borussia Dortmund's final two Bundesliga matches, as they missed out on their first league title since 2012.
And even though he is not available for selection, Bellingham, who is set to join Real Madrid, will spend time at the national football centre to continue his rehabilitation.
The rest of the England squad have already started to report for international duty ahead of the June fixtures.
While most of the group reported on Sunday, West Ham star Declan Rice is expected to arrive in the coming days after guiding the Hammers to Europa Conference League glory.
Meanwhile Manchester City's England stars will also report in the next few days after their Champions League celebrations are done and dusted.