Michael Morton pulled off the catch after Windies opener Kieran Powell lofted a six over mid-wicket off the bowling of Mitchell McClenaghan.
The prize was put up by beer company Tui and Morton fulfilled the requirements of wearing a company T-shirt and taking the ball one-handed.
"It's pretty unbelievable," he told Sky Sport.
"I was sitting next to my dad and he just yelled. I jumped up, stuck the hand down and somehow it just stuck."
Morton, who "used to" play cricket, said he always sat at the same grassed area when he went to matches at Seddon Park.
He wasn't sure what he would do with the money.
"I'll have to tell the missus first," he said.
Morton is the first winner in Tui's Catch a Million promotion during the Black Caps' summer of one-day and Twenty20 internationals.
There are seven further fixtures where the same prize will be up for grabs.