Hudson had hoped Reid would recover from the injury that has sidelined the West Ham centre-back for several weeks but Tuesday's friendly in Seoul comes too soon for the 26-year-old.
All Whites striker Chris Wood will deputise in Reid's absence.
"We gave Winston until the very last moment to see if he would be able to be part of the camp here in Seoul," Hudson said.
"It's a shame his injury hasn't fully healed and he won't be part of this trip. West Ham have been very co-operative and we had the chance to bring Winston out here to be part of the camp off the field, which we decided against.
"We will now move forward in our planning and it opens up an opportunity for another member of the squad to stake their claim."
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