Chapman sustained the injury while fielding during the first ODI in Napier and a subsequent MRI scan revealed a grade one tear which will require a short period of rehabilitation.
Chapman, who scored a career-best 132 in the series opener at McLean Park, will return to Auckland for rehabilitation with the aim to be available for the third and final ODI at Bay Oval on Saturday.
Top-order batter Tim Seifert will replace Chapman in the squad in Hamilton.
Seifert joins the squad off the back of a memorable T20I series against Pakistan where he topped the run-scoring charts with 249 runs, averaging 62.
Coach Gary Stead said the injury was unfortunate for Chapman and the team.
"We're thankful that the hamstring injury is only minor, so we're hopeful that Mark will be able to complete his rehabilitation and be available for the final match of the summer in the Mount."
While ODI squad selection preference was given to players on full national and domestic contracts, Stead said Seifert's recent form had warranted his selection.
"With several new faces in this squad, it's great to be able to call on a player of Tim's experience," he said.
"He's in good form after a great T20 series and he provides another strong top-order batting option heading into an important match."
New Zealand lead the three-match ODI series 1-0 after winning the T20 series 4-1.
