International Friendly: China v New Zealand
The West Ham defender has been ruled out of the China clash, as well as a meeting with Thailand, due to a niggling injury.
Hudson said he was sad to be without Reid, but wished him a quick recovery.
"Winston is a big loss. He's a top footballer, a top captain and a good man," he said.
"Hopefully he has a quick recovery and we look forward to him being back with us in our next games."
Hudson's only match in charge resulted in a 3-1 loss against Uzbekistan in September.
Reid backed the 33-year-old American to help New Zealand improve after they failed to qualify for the World Cup.
The loss to Uzbekistan marked New Zealand's seventh straight match without a win.
"I respect the environment that we are trying to build with the national team, a winning environment and this requires a 100 per cent dedication on and off the pitch," Reid said.
"I look forward to following the team in these upcoming games and even more to take part again in March."
China host the friendly in Nanchang, and come into the clash in far better form.
The Asian nation is unbeaten in four matches and were 2-1 victors over Paraguay in their most recent outing.
Alain Perrin's side are preparing for next year's Asian Cup and will be eager to continue building their form.