The 25-year-old, who is yet to play in a competitive international, has won two caps, both in friendly matches against the Netherlands.
"He doesn't want to play international football, which is a disappointment from our point of view," said Wales manager Chris Coleman.
"But he's made that decision, and we have to abide by that."
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Wales are third in World Cup qualifying group D, four points behind leaders Serbia.
They travel to Serbia for their next qualifier on Sunday, 11 June after naming a youthful pre-match training camp that included Exeter's 16-year-old Ethan Ampadu.
Coleman added: "We'll get on with the squad of players, the squad who want to play and represent Wales.
"There's nothing we can do with Paul, who's decided that international football is not the path he wants to go down."
Newcastle-born Dummett was included in a pre-Euro 2016 training camp but was not selected in the squad for the tournament in France. He has not featured at all during the current World Cup qualifying campaign.
"Sometimes you have to be patient especially because the team we have at the moment has been hugely successful," Coleman added.
"It's a shame because he's a good player. I haven't spoken to Paul. His agent rang me up to give me the news.
"I was disappointed, but if he doesn't want to persevere with it then that's his choice. We've got to look after the players who want to play for us."
Newcastle United defender Paul Dummett has made himself unavailable to play for Wales.