"He (Henry) is not a cheat, I know him well," the former France playmaker, who was sent off for headbutting Italy defender Marco Materazzi in the 2006 World Cup final, told French television channel Canal Plus.
"He will get over this," Zidane added. "He made a mistake, like I made a mistake, even if I'm not making any comparisons. We all make mistakes."
Henry, Zidane said, had apologised by admitting he had handled the ball.
"The fact he said there was a handball means he has apologised," Zidane said. "I'm not saying it was nothing but it was handball, that's it."
France captain Henry handled the ball setting up William Gallas's extra-time equaliser in Wednesday's 1-1 draw in Paris that sent France to the World Cup with a 2-1 aggregate win.
The French Football Federation (FFF) has ruled out a replay, saying world governing body FIFA's decision that the result should stand was final.
'My shot was so clearly over the line – like Lampard against Germany. I was more gutted for my mates, as they’d backed me as the first goalscorer!’: England star reflects on agony of not being awarded maiden Three Lions goal
Donald Trump vs the United States: A timeline of the president's spat with the national team
