The Costa Rica striker found the back of the net as his country claimed a 3-1 win over Uruguay in their opening World Cup match.
Henry has been impressed by what he has seen from the 21-year-old and would like Arsene Wenger to give him a run in the first team.
"Joel Campbell is a great player. He can pass the ball well and smells the goal," he told BBC Sport.
"We are all waiting to see him in an Arsenal shirt. Hopefully he will be a player Arsene Wenger likes because I would love to see him play for Arsenal."
Campbell joined Arsenal from Deportivo Saprissa in 2011 but has not played for the club, having spent the past three seasons on loan.