Henshaw battled for the top prize with Ukrainian Viktoriia Savstova but was an agonising 0.03s short.
However, Henshaw was delighted with her achievement and "chuffed" to have a medal around her neck at all.
"I couldn't see [Savstova] at all," Henshaw said. "I knew she was there or thereabouts. I put my head down and tried to touch first, but I'm so happy just to get on the podium, I really am.
"I'm so chuffed because I know what it's like to finish outside the medals and I didn't want that to happen here in front of everyone.
"I tried my hardest and I can walk away with my head held high with my silver medal."
Henshaw's teammate Elizabeth Johnson took bronze in the same race.