"Given the depth and the longevity of our relationship, which covers trade, defence and economies, I don't imagine there would be any change whatsoever in the relationship with New Zealand," said Mr Robinson.
There are about 4000 New Zealanders living in Singapore and 5400 Singapore-born residents in New Zealand.
Singaporeans living in New Zealand can register to vote, but the closest designated overseas polling station for Kiwi-Singaporeans is the High Commission offices in Australia.
Singaporean Celeste Lee, from Botany in Auckland, was visiting family in Singapore when the elections were announced last week.
Mrs Lee will be extending her stay to vote in the election, her first in over 20 years.
"Friends tell me why vote because I no longer live here, but I am still a Singapore citizen and all my family are here," she said.
"Who leads this country will affect me in more ways than one."
New Zealand was one of the first countries to recognise Singapore's Independence in 1965 and the first country to sign a bilateral free trade agreement with Singapore, which came into effect in 2001.
It was one of just two countries, the other being India, which flew flags at half mast to mark Lee Kuan Yew's passing on March 23.
Singapore Prime Minister Lee Hsien Loong, the son of the late Mr Lee, said the coming election was about picking leaders who can take Singapore forward over the next 20 years.
Leaders of Singapore's main opposition party, the Workers Party, also have close family links in New Zealand.
Party chair, MP Sylvia Lim's sister is a senior ANZ bank manager in Auckland and organising secretary, MP Pritam Singh has a cousin working as a journalist at the New Zealand Herald.
- Lincoln Tan travelled to Singapore with the help of Asia New Zealand Foundation