The 24-year-old took four for 42 and two for 21 in the first two matches against Pakistan, dismissing the world's number one 50-over batsman Babar Azam on both occasions.
The fixture, which is the final game of a three-match ODI series between the two sides, is slated to be played on 13 July.
Stone's latest setback of an injury-blighted career has led to the uncapped George Garton being called into England's one-day international squad for the upcoming series against Sri Lanka.
England vs New Zealand: Matt Henry, Neil Wagner run through English batting order as Black Caps sniff victory on Day 3
England, on a good batting pitch, were 122-9 in their second innings at stumps on the third day — just 37 runs ahead of New Zealand with one wicket standing and two days left to play.
The 29-year-old opener had launched his Test career with a stunning 200 on debut in the first of this two-match series at Lord's last week.
Follow live score and updates from Day 1 of the second Test between England and New Zealand on our live blog.
England vs New Zealand: Ollie Robinson suspended from international cricket for 'racist and sexist' tweets
The paceman led England's attack with 4-75 in the first innings at Lord's and followed up with 3-26 in the second while in between making a useful 42 with the bat.
Under current guidelines, smaller outdoor venues are only permitted to be at 25 percent capacity, but the stadium will be 70 percent full for the second Test against the Black Caps, which takes place between 10 and 14 June.
Former England batsman Ian Bell says 'not ideal to play without the fans' but players need to get used to it
England and Wales Cricket Board (ECB) had to suspend all cricket activities till 1 July due to the coronavirus outbreak and the governing body is now looking to resume the game this summer behind closed doors.
My Favourite Match: A tie, a lie and complete disregard for maths - How Australia vs South Africa '99 World Cup semi-final ruined my childhood
For a generation of Indians, the epic 1999 World Cup semi-final between Australia and South Africa remains one of the foremost matches we were heavily invested in as a neutral, or perhaps that’s the one game we remember for its sheer ludicrousness.
T20 Blast: Captain Simon Harmer's all-round performance helps Essex beat Worcestershire in dramatic final
Essex captain Simon Harmer produced a match-winning cameo with the bat to lead his team to victory over Worcestershire on the final ball of Saturday's T20 Blast final.
Ashes 2019: Australia coach Justin Langer rules out bouncer battle at Headingley, says team focussed on winning third Test
Australia coach Justin Langer has told his side to avoid being drawn into a bouncer battle after Steve Smith was ruled out of the third Ashes Test against England.
Ashes 2019: Marnus Labuschagne's gritty fifty overshadows Ben Stokes' ton as second Test ends in draw
Australia, set an unlikely 267 to win in a minimum of 48 overs after England captain Joe Root's declaration, finished on 154-6.
Ashes 2019: Joe Root says England desperate to win second Test; Tim Paine recalls making debut at Lord's nine years ago
Root's men head into the second Test at Lord's starting on Wednesday 1-0 down in a five-match series following a 251-run hammering by Australia at Edgbaston last week and knowing another defeat would leave their hopes of regaining the Ashes hanging by a thread.
England all-rounder Moeen Ali is taking a short break from all forms of cricket following his omission from the England squad for the second Ashes Test.
But should Steve Smith be compared to the greatest of them all, Don Bradman?
England are set to field a revamped attack featuring fast bowler Jofra Archer as they try to finally get Australia's batting star Steve Smith out cheaply and level the Ashes in the second Test at Lord's.
Ashes 2019: Pat Cummins feels fresh after 10-day break before second Test, says he wants to play all five Tests against England
The 26-year-old took four for 32 in England’s second innings at Edgbaston as Australia romped to a 251-run victory in the first test — his maiden away outing in cricket’s oldest international rivalry.
Langer said it's credit to Smith that he began his career as a spinner and later transformed into the best batsman in the world.
James Anderson has been ruled out of the second Ashes Test, with England uncertain when he will be fit to return from an injured right calf.