Skyes, 23, was included in three Northern Ireland squads by former manager Michael O’Neill but did not make his senior debut.
The former Glenavon player earned 11 Northern Ireland under-21 caps under O’Neill’s successor Ian Baraclough, but has now told the Irish Football Association he does not wish to be selected again.
The IFA is understood to be disappointed by the decision but will not be making a comment.
The news comes a day before Baraclough is due to name his Northern Ireland squad for his first games in charge – away to Romania and at home to Norway in the Nations League next month. Republic boss Stephen Kenny will also name his squad for games against Bulgaria and Finland on Monday.
Sykes earned his first Northern Ireland call-up in May 2019 and was back in the squad for games against Luxembourg and Germany in September.
He was also in the squad for the Euro 2020 qualifying play-off semi-final against Bosnia-Herzegovina when it was named by O’Neill in March, though that fixture was postponed due to the coronavirus pandemic and is now due to be played in October.
The Belfast-born Sykes impressed as a teenager with Glenavon before joining Oxford in January 2019, helping them to the League One play-off final last season and scoring in their 2-1 defeat to Wycombe at Wembley last month.