The team signed one of Wood's test shirts and presented that, alongside a bat, to Sheeran when they popped up to his corporate box.
He had less time with the New Zealanders, but generated no less interest as budding guitarists Trent Boult and Kane Williamson, and fast bowler Matt Henry stopped for a chat.
The Shape of You and Thinking Out Loud singer posted a picture of himself at Eden Park. He was also given a shirt by the Black Caps.
The Black Caps posted on their Instagram account: "Thanks for joining us at our first Day-Night Test @teddysphotos. Good luck with the tour and we hope you enjoy the shirt!"
New Zealand captain and part-time guitarist Williamson said: "It was fantastic to meet him, a humble guy who enjoys his cricket. It was cool for him to come along today and watch a little bit."
"A few of the lads chatted to him for a while, but it was nice after a couple of average days to meet someone of his calibre," England pace bowler James Anderson said.
"I think his Dad likes cricket and he's here. There are a few songs on the team playlist, but luckily they weren't playing when he came in [to the dressing room]."
Earlier, Williamson notched up his 18th test century to surpass Martin Crowe and Ross Taylor and become the leading New Zealand test centurion.