This adds to the nerves surrounding other All Whites Premier League star Chris Wood, who left the field 20 minutes into his Burnley side's 3-0 defeat at Manchester City last Sunday with a hamstring injury.
Burnley manager Sean Dyche said Wood was "touch and go" to play in Tuesday's clash against Newcastle.
"Woody has a chance, but he is touch and go for Monday," Dyche told the Burnley Express.
"He's responded well to treatment, and it's not a deep-seated problem, but we have to make sure with him."
A good sign for the All Whites is that both Reid and Wood aren't taking any chances with their injuries, which will please All Whites coach Anthony Hudson.
The first leg of the World Cup qualifying playoff is on Saturday 11 November at Westpac Stadium in Wellington.