Isner will miss the tournament to spend more time in Melbourne to prepare for the Australian Open which starts on January 19.
The defending Heineken Open champion is currently in Perth playing the Hopman Cup exhibition event.
Heineken Open tournament director Karl Budge says he is frustrated that Isner chose to play an exhibition event rather than an ATP tournament.
"As you can imagine, we were very disappointed to receive this news but unfortunately it's something we have little control over."
Isner released a statement concerning his withdrawal from the event.
"I am really disappointed to withdraw from Auckland, one of my favourite stops of the year," he says.
"As much as I would like to be competing in Auckland to defend my title, I feel at this time it is best for me to hit the practice courts in advance of the Australian Open."
Monfils has cited "personal reasons" as the reason for his withdrawal.
In a statement, the Frenchman said that he is "deeply disappointed for the fans since I love the tournament and keep great memories of my last visit in New Zealand."