The Everton defender arrived in the training camp with the problem.
The Everton defender arrived in the training camp with the injury but had hoped to be fit for the fixture in Budapest.
However, following further assessment, the 32-year-old will return home as a precaution, according to a statement from the Football Association of Ireland.
Ireland finally enjoyed their first victory under manager Stephen Kenny – at the 12th attempt – by coming from behind to win 4-1 in Andorra on Thursday.
Coleman, who was appointed skipper in September 2016 following Robbie Keane’s international retirement, played no part in that game.
The rest of Kenny’s squad will travel to the Hungarian capital later on Sunday from their training base in Girona, Spain.
Having failed to qualify for Euro 2020, the midweek friendly is Ireland’s final scheduled outing before their 2022 World Cup qualifying campaign resumes away to Portugal on September 1.