Killen is a key part of the All Whites attack in tandem with Shane Smeltz as New Zealand look ahead to their crucial FIFA World Cup qualifiers in October and November.
Killen's absence for the friendly on the 9 September gives Plymouth Argyle forward Rory Fallon and West Bromwich Albion striker Chris Wood an opportunity to stake their claims for the play-off matches, All Whites coach Ricki Herbert said.
The Amman friendly is New Zealand's final chance before taking on either Bahrain or Saudi Arabia in the home and away qualifying matches, with the winners going through to next year's FIFA World Cup in South Africa.
"This match is very important; it's certainly a dress rehearsal for the opening qualifier on 10 October," Herbert said. "It'll be quality time, five days together with a very competitive game in an area of the world we'll be coming back to in a month's time."
New Zealand's opponents for the FIFA World Cup qualifiers will be decided when Bahrain and Saudi Arabia play home and away Asian Zone qualifying matches on Saturday and Wednesday.