The 21-year-old Wimbledon quarter-finalist fought all the way in the second set, falling 2-0 and 5-3 behind but battling back to 5-5 and almost snatching the lead.
He netted a crucial and relatively easy forehand down the line which would have given him a 6-5 advantage. Instead his opponent took the game and the second tie-break of the evening was set up when Henman won his serve to draw level.
Woodbridge demonstrated the same steely edge he had shown in the first set and won the showdown 7-5 to claim victory on his fifth match point. He had won the first-set tie-break 8-6.
A disappointed Henman put a brave face on things as he stopped to sign autographs for the dozens of British fans who had turned out to cheer him on.
He said: "Of course I am disappointed, but you can't beat everyone. I would have liked to have gone further but it is now time to concentrate on the doubles. The whole thing has been a great experience and something I will remember as very special for a long time.
"It has been a lot better than I had expected coming in knowing nothing. There has been a great atmosphere everywhere, especially in the Olympic village."
The unheralded Japanese Ai Sugiyama beat Martina Hingis in straight sets in the second round of the women's singles. Sugiyama, ranked 24th in the world, won 6-4, 6-4.
Hingis, 15 years old and 15th seed, held a 3-0 lead in the second set but the 21-year-old Sugiyama hit back, moving well and making impressive winners.