Manager Michael O’Neill has been preparing for Sunday’s opening Group F clash and was expected to trim his 26-man squad by at least two before they fly out to Budapest.
But the decision was taken out of his hands as Hull City defender Bruce has withdrawn after his wife went into labour, while uncapped MK Dons midfielder Reeves has suffered a hamstring problem.
O’Neill lost two squad members before the training camp as Liverpool full-back Ryan McLaughlin is nursing a knee problem and Brentford winger Stuart Dallas pulled out with a leg complaint.
Northern Ireland will also face Greece, Romania, Finland and the Faroe Islands as they target an improved performance in this latest qualifying campaign.
They could only muster a fifth-place finish in their World Cup group after a solitary win from 10 matches.
Watch Northern Ireland's European Qualifier away to Hungary live on Sky Sports 3 HD on Sunday, with coverage underway from 4.45pm.