"It's disappointing he is not coming because he is such an important player, he is a great character and I know how much he was looking forward to being here. I hope he gets fit really soon.
"But with regards to the team we have been in this position many times. We have got a good squad, we are adaptable and we have enough in this squad to deal with this tour so we are prepared for this."
Meanwhile, Patterson has failed to overcome a hamstring injury and will also miss the tour.
The 20-year-old, who plays for Ipswich Town FC in the Championship, will be replaced by Alex Rufer in the squad for the OFC Stage Three Qualifiers.
Rufer, an attacking midfielder from the Wellington Phoenix, has earned two international caps since making his debut for New Zealand back in 2015.
Hudson said it was a shame for Patterson who has developed well in recent time, including scoring his maiden international goal against the USA last October.
"I'm gutted for Monty as I know he was really looking forward to meeting up with the national team," said Hudson.
"But as always, it becomes an opportunity for someone else. I'm pleased to bring Alex in and he's a natural replacement in midfield. I'm well aware of his quality, and when I saw him train down at the Phoenix a while back he was one of the best players on the pitch. Everyone I speak to down there tells me how well he's been doing too. So I'm glad he's back involved."
The All Whites have begun assembling in Wellington for a four day training camp ahead of facing Fiji on 25 March in Lautoka. The return home leg is in Wellington on Tuesday 28 March.