All-rounder Stokes was named man of the match as England broke Kiwi hearts in the Lord’s final this month.
The 28-year-old was born in New Zealand but moved to England aged 12.
“It would not sit right with me to be nominated for this prestigious award,” said Stokes.
“There are people who deserve this recognition more and have done a lot more for the country of New Zealand.
“I have helped England lift a World Cup and my life is firmly established in the UK.”
The New Zealand public nominates “inspirational KiWIS” for the award – those who they believe have made a “significant contribution to our nation and make us proud of our country”.
Previous winners have included former New Zealand Rugby union captain Richie McCaw, filmmaker Taika Waititi and mental health campaigner Mike King.
Stokes added he was “proud” of his New Zealand and Maori heritage, but called for Williamson – who was named player of the tournament at the World Cup – to win.
“He should be revered as a Kiwi legend,” he said. “He led his team in this World Cup with distinction and honour.
“He was the player of the tournament and an inspirational leader of men. He shows humility and empathy to every situation and is an all-round good bloke.
“He typifies what it is to be a New Zealander. He would be a worthy recipient of this accolade. New Zealand, fully support him. He deserves it and gets my vote.”