Henry, on loan from Reading, slotted home Scott Barron's cross to condemn Huddersfield to their first home defeat since November.
The visitors almost went ahead in the 11th minute as Henry's inviting cross was nodded onto the crossbar by Huddersfield's Andy Butler before being cleared.
Huddersfield started well after the restart and Lionel Ainsworth fired wide when it was easier to score in the 53rd minute.
Millwall broke the deadlock with 20 minutes remaining as Marc Laird stroked home David Martin's pass.
But Huddersfield hit back moments later as Gary Roberts scored his second goal in as many matches before the lively Henry snatched a dramatic winner for the visitors.