The person arrived two weeks ago, and tested positive for the virus once in New Zealand.
They are staying in managed isolation in Auckland.
The tiny island nation has not had any previously reported cases of Covid-19.
About 14,000 people live across the Tuvalu archipelago, and UN data shows that 12,114 Covid-19 vaccine doses have been administered there.
The New Zealand Ministry of Health said this case was one of three new incoming border cases that were reported yesterday.
Another 126 community cases were also reported in New Zealand yesterday.