She told the Otago Daily Times she was in Searle Lane's Habana bar with friends - they were the only people there - at about 10.30pm when Sheeran walked in with a group.
"I didn't notice him until my friend said 'wow, that guy looks just like Ed Sheeran!'.
Sheeran swore off social media, emails and his phone last December.
He said on Twitter: "I've had such an amazing ride over the last five years but I find myself seeing the world through a screen and not my eyes so I'm taking this opportunity of me not having to be anywhere or do anything to travel the world and see everything I missed."
Sheeran won two Grammy Awards last year, for best pop solo performance and song of the year, for the song Thinking Out Loud.
Sales of his second album, X, passed 10 million copies last August.