A brief statement on the Northern Irish Football Association's official website on Thursday confirmed the news, leaving Michael O'Neill with a squad of 23 to choose from for the clash in Budapest.
Hull City defender Bruce withdrew after his wife went into labour while Reeves, who was influential for MK Dons in their 4-0 dismantling of Manchester United in the League Cup last month, has pulled out due to a hamstring problem.
The duo's withdrawals come on the back of two more absentees which were announced on Tuesday.
Brentford's Stuart Dallas was ruled out with a leg injury, and was replaced by Preston North End's Andy Little, while Ryan McLaughlin of Liverpool will not feature due to a knee problem.
Sunday's game in the Hungarian capital is Northern Ireland's first of their qualification campaign, having been drawn in Group F, which also includes Finland, Greece, Romania and the Faroe Islands.
