Instead Mr Apiata, a Victoria Cross recipient, greeted the fifth in line to the throne with a hongi - a traditional Maori greeting.
Mr Apiata and Prince Harry crossed paths at the Invictus Games, being held in Toronto.
They enable wounded, injured or sick armed services personnel and veterans to participate in sports including wheelchair basketball, sitting volleyball and indoor rowing.
Earlier this week Mr Apiata was captured on camera in an Invictus Games T-shirt, a pair of shorts and what appear to be jandals, performing the NZ Defence Force's haka in the stands in honour of New Zealand's first medal winner.
Whangarei navy officer Dan Crawford, 26, claimed bronze in the Men's IT7 1500m.
As at the end of yesterday New Zealand held 11 medals - three gold, four silver and four bronze.
The haul is two more than the team's total at the 2016 games.