The British tennis star was a surprise semi-finalist at the All England Club and Henman is keen to see how the player will fare at the US Open later this summer.
The six-time Grand Slam semi-finalist told Sky Sports: "He's still got a lot of areas that he can improve in his game and I think that's exciting when you know you're young.
"I can't wait to watch him. We need those British players at the top of the game and he's got a great opportunity."
Henman believes that Fery's Wimbledon run was a welcome boost for British tennis after Emma Raducanu and Jack Draper were both forced to withdraw from the tournament due to injury.
He said: "We needed that because those first couple of days were pretty rough for British tennis, but it was brilliant to see Arthur play so well and if Emma [Raducanu] and Jack [Draper] can be back fit, then there's also Katie Boulter, Cam Norrie, while Jan Choinski has just broken into the top 100 - he's 75 in the world now - so you want those British players creating stories at the biggest events."
Fery has risen to 36th in the world rankings on the back of his Wimbledon performances and Henman thinks that playing in Grand Slam and Masters 1000 events will help the player establish himself in the game.
The former British number one explained: "He started the year at 185 in the world, qualified in Melbourne and then has continued to improve his ranking - then getting a wild card at Wimbledon ranked 114 and winning five matches getting to the semi-finals it was an incredible performance - and I think it also shows the fine margins between these top players.
"If you're in the top 250 in the world you're an extremely good player and on your day you've got a chance of beating anyone, so huge for him to be 36 in the world now getting to the other Grand Slams and Masters 1000, so he's got an opportunity to really plan his schedule moving forward."