The Hammers centre-back got through the full 90 minutes as the All Whites kept a clean sheet in goalless first leg at the Westpac Stadium in Wellington on Saturday.
New Zealand coach Anthony Hudson is confident his skipper will have no problem starting the second leg in Lima.
"It wasn't muscular, it was just a knock," he said.
"This morning we've had a good recovery session, we've had a good session with the subs. Now what we need to do in the next couple of days is make sure we do everything possible to get our best team on the pitch."
Reid was satisfied with his, and his team's, performance on Saturday.
"We’ve been close to getting a result before against the so-called bigger teams," the Hammers defender told Fox Sports.
"Today, for me, was about keeping a clean sheet at the back and giving ourselves an opportunity in the second leg. We’ve certainly done that."