Henry was involved in the only goal of the game as Ambroise Oyongo headed down his corner kick for Bradley Wright-Phillips to score the only goal.
Wright-Phillips nearly doubled the lead but was foiled by Wojciech Szczesny, who is set to compete for a starting berth with Wenger's latest signing, Colombia goalkeeper David Ospina.
Arsene Wenger fielded a strong starting line-up and Jack Wilshere came close to an equaliser, but the England midfielder was denied by home goalkeeper Luis Robles.
Wenger made a number of changes at half-time with Mathieu Flamini and Abou Diaby introduced along with five other changes.
Arsenal's best chance of the second-half fell to 18-year-old striker Chuba Akpom as he did well to work some space only to shoot straight at Robles.
Wenger was not too concerned about his side's inability to score, stressing that he did not have a full squad available.
He said: “We had no Giroud, no Walcott, no Sanchez and no Podolski. Akpom did well but he’s a young boy and he has to learn a lot but he has potential.
“As long as you don’t score it’s not good but you can play with three No 9s and you don’t score sometimes. We were dominated physically in the first half, we came back into it in the last 10 minutes their keepers made a few saves and our combinations were better. We lacked a bit of pace without any centre forward.”
Wenger did feel that the North American tour had been worthwhile, adding: “For us it was a great experience, everybody enjoyed it and nobody wants to go home.
“It was a short trip but a very exciting one because New York is a special city. But what is even more special for us is how popular football is now.
“The values we stand for are shared here and everybody was very friendly and everybody respects what we try to do.
“One of the values we have to stand up for as well is when your opponent is better than us, we have to say ‘well done’ and today that was the case.”