Ibrahimovic, 35, has gone six league games without scoring a goal for United – his longest goalless run in domestic league football since 2007.
The Red Devils have only won one of those six matches and have failed to score in their last three.
Ibrahimovic had 12 shots on goal in the Red Devils' 0-0 draw with Burnley at Old Trafford on 29 October, but missed some gilt-edged chances and were frustrated by Clarets goalkeeper Tom Heaton, who made a string of brilliant saves to deny the hosts.
Speaking on Sky Sports, Henry said Ibrahimovic's confidence would have been dented by his goal drought.
"Sometimes it's okay if you don't score but your team still wins but he knows he's had great opportunities to score goals in important games," the former Arsenal captain said.
"Yes, it does affect you but I would still back him to deliver for United because of the player he was and he is still. It hasn't happened for him recently for United, but he needs to find a way to score goals because they need that.
"Does it affect him? Yes, he's a human being but he has the right tools in his mind to recover from that."
The Burnley result extended United's winless run in the league to four matches and leaves the club eight points behind leaders Manchester City after 10 fixtures.
The Red Devils' next assignment sees them travelling to Istanbul to take on Fenerbahce in the Europa League on 3 November, with Ibrahimovic likely to be rested for the encounter.
Henry added: "It's the first time [Ibrahimovic] has found himself in this situation in his career.
"He's going to have to deal with it. I know he has the character and the ability to deal with it but it will be better for him if it happens sooner rather than later."